![Page 1: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/1.jpg)
Section 1.9: Proportionality, Power Functions, AndPolynomials
We have already studied:
I Linear functionsI Exponential functionsI Natural logarithm
In this section, we will study a few more class of functions:I ProportionalityI Power functionsI Polynomial functions
![Page 2: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/2.jpg)
Section 1.9: Proportionality, Power Functions, AndPolynomials
We have already studied:I Linear functions
I Exponential functionsI Natural logarithm
In this section, we will study a few more class of functions:I ProportionalityI Power functionsI Polynomial functions
![Page 3: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/3.jpg)
Section 1.9: Proportionality, Power Functions, AndPolynomials
We have already studied:I Linear functionsI Exponential functions
I Natural logarithmIn this section, we will study a few more class of functions:I ProportionalityI Power functionsI Polynomial functions
![Page 4: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/4.jpg)
Section 1.9: Proportionality, Power Functions, AndPolynomials
We have already studied:I Linear functionsI Exponential functionsI Natural logarithm
In this section, we will study a few more class of functions:I ProportionalityI Power functionsI Polynomial functions
![Page 5: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/5.jpg)
Section 1.9: Proportionality, Power Functions, AndPolynomials
We have already studied:I Linear functionsI Exponential functionsI Natural logarithm
In this section, we will study a few more class of functions:
I ProportionalityI Power functionsI Polynomial functions
![Page 6: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/6.jpg)
Section 1.9: Proportionality, Power Functions, AndPolynomials
We have already studied:I Linear functionsI Exponential functionsI Natural logarithm
In this section, we will study a few more class of functions:I Proportionality
I Power functionsI Polynomial functions
![Page 7: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/7.jpg)
Section 1.9: Proportionality, Power Functions, AndPolynomials
We have already studied:I Linear functionsI Exponential functionsI Natural logarithm
In this section, we will study a few more class of functions:I ProportionalityI Power functions
I Polynomial functions
![Page 8: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/8.jpg)
Section 1.9: Proportionality, Power Functions, AndPolynomials
We have already studied:I Linear functionsI Exponential functionsI Natural logarithm
In this section, we will study a few more class of functions:I ProportionalityI Power functionsI Polynomial functions
![Page 9: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/9.jpg)
Proportionality
DefinitionWe say y is (directly) proportional to x if there is a nonzeroconstant k such that
y = kx
This k is called the constant of proportionality.
. . . proportional to . . . ≈ . . . a (nonzero) constant multiple of . . .
Example“y is proportional to x” means exactly y = kx for some k , 0.
![Page 10: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/10.jpg)
Proportionality
DefinitionWe say y is (directly) proportional to x if there is a nonzeroconstant k such that
y = kx
This k is called the constant of proportionality.
. . . proportional to . . . ≈ . . . a (nonzero) constant multiple of . . .
Example“y is proportional to x” means exactly y = kx for some k , 0.
![Page 11: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/11.jpg)
Proportionality
DefinitionWe say y is (directly) proportional to x if there is a nonzeroconstant k such that
y = kx
This k is called the constant of proportionality.
. . . proportional to . . . ≈ . . . a (nonzero) constant multiple of . . .
Example“y is proportional to x” means exactly y = kx for some k , 0.
![Page 12: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/12.jpg)
ExampleThe heart mass of a mammal is proportional to its body mass.Write a formula for heart mass, H, as a function of body mass, B.
Solution:H = kB
If a human with a body mass of 70kg has a heart mass of0.42kg, find the constant of proportionality.Solution:
0.42 = k · (70)
k =0.4270
= 0.006
![Page 13: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/13.jpg)
ExampleThe heart mass of a mammal is a constant multiple of its bodymass. Write a formula for heart mass, H, as a function of bodymass, B.
Solution:H = kB
If a human with a body mass of 70kg has a heart mass of0.42kg, find the constant of proportionality.Solution:
0.42 = k · (70)
k =0.4270
= 0.006
![Page 14: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/14.jpg)
ExampleThe heart mass of a mammal is a constant multiple of its bodymass. Write a formula for heart mass, H, as a function of bodymass, B.Solution:
H = kB
If a human with a body mass of 70kg has a heart mass of0.42kg, find the constant of proportionality.Solution:
0.42 = k · (70)
k =0.4270
= 0.006
![Page 15: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/15.jpg)
ExampleThe heart mass of a mammal is a constant multiple of its bodymass. Write a formula for heart mass, H, as a function of bodymass, B.Solution:
H = kB
If a human with a body mass of 70kg has a heart mass of0.42kg, find the constant of proportionality.
Solution:
0.42 = k · (70)
k =0.4270
= 0.006
![Page 16: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/16.jpg)
ExampleThe heart mass of a mammal is a constant multiple of its bodymass. Write a formula for heart mass, H, as a function of bodymass, B.Solution:
H = kB
If a human with a body mass of 70kg has a heart mass of0.42kg, find the constant of proportionality.Solution:
0.42 = k · (70)
k =0.4270
= 0.006
![Page 17: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/17.jpg)
ExampleThe area A of a circular disk is proportional to the square of itsradius r. Write a formula for A as a function of r.
Solution:A = kr2
Indeed, we know that this constant of proportionality is thefamous constant π.
![Page 18: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/18.jpg)
ExampleThe area A of a circular disk is a constant multiple of the squareof its radius r. Write a formula for A as a function of r.
Solution:A = kr2
Indeed, we know that this constant of proportionality is thefamous constant π.
![Page 19: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/19.jpg)
ExampleThe area A of a circular disk is a constant multiple of the squareof its radius r. Write a formula for A as a function of r.Solution:
A = kr2
Indeed, we know that this constant of proportionality is thefamous constant π.
![Page 20: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/20.jpg)
ExampleThe area A of a circular disk is a constant multiple of the squareof its radius r. Write a formula for A as a function of r.Solution:
A = kr2
Indeed, we know that this constant of proportionality is thefamous constant π.
![Page 21: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/21.jpg)
Inverse Proportionality
DefinitionSimilarly, we say y is inversely proportional to x if there is anonzero constant k such that
y =kx
I.e.,x · y = k
So we can also say two quantities are inversely proportional iftheir product is a (nonzero) constant.
![Page 22: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/22.jpg)
Inverse Proportionality
DefinitionSimilarly, we say y is inversely proportional to x if there is anonzero constant k such that
y =kx
I.e.,x · y = k
So we can also say two quantities are inversely proportional iftheir product is a (nonzero) constant.
![Page 23: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/23.jpg)
ExampleThe time, T, taken for a journey is inversely proportional to thespeed of travel v. Write a formula for T as a function of v.
Solution:T =
kv
for some k , 0.
ExampleThe amount G of gasoline one can purchase with $20 isinversely proportional to the price P of each gallon of gasoline.Write a formula for G as a function of P.Solution:
G =kP
for some k , 0.
![Page 24: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/24.jpg)
ExampleThe time, T, taken for a journey is inversely proportional to thespeed of travel v. Write a formula for T as a function of v.Solution:
T =kv
for some k , 0.
ExampleThe amount G of gasoline one can purchase with $20 isinversely proportional to the price P of each gallon of gasoline.Write a formula for G as a function of P.Solution:
G =kP
for some k , 0.
![Page 25: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/25.jpg)
ExampleThe time, T, taken for a journey is inversely proportional to thespeed of travel v. Write a formula for T as a function of v.Solution:
T =kv
for some k , 0.
ExampleThe amount G of gasoline one can purchase with $20 isinversely proportional to the price P of each gallon of gasoline.Write a formula for G as a function of P.
Solution:G =
kP
for some k , 0.
![Page 26: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/26.jpg)
ExampleThe time, T, taken for a journey is inversely proportional to thespeed of travel v. Write a formula for T as a function of v.Solution:
T =kv
for some k , 0.
ExampleThe amount G of gasoline one can purchase with $20 isinversely proportional to the price P of each gallon of gasoline.Write a formula for G as a function of P.Solution:
G =kP
for some k , 0.
![Page 27: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/27.jpg)
Power Function
DefinitionWe say that f (x) is a power function of x if f (x) is proportionalto a constant power of x. I.e.
f (x) = k · xp
for some constants k, p , 0.
Example
5x3 2x100 3x12 4x1.349 9xπ
are all power functions of x
![Page 28: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/28.jpg)
Power Function
DefinitionWe say that f (x) is a power function of x if f (x) is proportionalto a constant power of x. I.e.
f (x) = k · xp
for some constants k, p , 0.
Example
5x3 2x100 3x12 4x1.349 9xπ
are all power functions of x
![Page 29: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/29.jpg)
Which of the following functions are power functions of x?
f (x) = 2x4 power function: k = 2, p = 4
f (x) = x = 1x1 power function: k = 1, p = 1
f (x) =1x= 1x−1 power function: k = 1, p = −1
f (x) =5x3 = 5x−3 power function: k = 5, p = −3
f (x) = 2x not a power function
f (x) = 2x4 + 1 not a power function
f (x) = 3√
x = 3x1/2 power function: k = 3, p = 1/2
f (x) = (3√
x)3 = 27x3/2 power function: k = 27, p = 3/2
f (x) =5
9x2 =59
x−2 power function: k =59
, p = −2
![Page 30: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/30.jpg)
Which of the following functions are power functions of x?
f (x) = 2x4
power function: k = 2, p = 4
f (x) = x = 1x1 power function: k = 1, p = 1
f (x) =1x= 1x−1 power function: k = 1, p = −1
f (x) =5x3 = 5x−3 power function: k = 5, p = −3
f (x) = 2x not a power function
f (x) = 2x4 + 1 not a power function
f (x) = 3√
x = 3x1/2 power function: k = 3, p = 1/2
f (x) = (3√
x)3 = 27x3/2 power function: k = 27, p = 3/2
f (x) =5
9x2 =59
x−2 power function: k =59
, p = −2
![Page 31: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/31.jpg)
Which of the following functions are power functions of x?
f (x) = 2x4 power function: k = 2, p = 4
f (x) = x = 1x1 power function: k = 1, p = 1
f (x) =1x= 1x−1 power function: k = 1, p = −1
f (x) =5x3 = 5x−3 power function: k = 5, p = −3
f (x) = 2x not a power function
f (x) = 2x4 + 1 not a power function
f (x) = 3√
x = 3x1/2 power function: k = 3, p = 1/2
f (x) = (3√
x)3 = 27x3/2 power function: k = 27, p = 3/2
f (x) =5
9x2 =59
x−2 power function: k =59
, p = −2
![Page 32: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/32.jpg)
Which of the following functions are power functions of x?
f (x) = 2x4 power function: k = 2, p = 4
f (x) = x
= 1x1 power function: k = 1, p = 1
f (x) =1x= 1x−1 power function: k = 1, p = −1
f (x) =5x3 = 5x−3 power function: k = 5, p = −3
f (x) = 2x not a power function
f (x) = 2x4 + 1 not a power function
f (x) = 3√
x = 3x1/2 power function: k = 3, p = 1/2
f (x) = (3√
x)3 = 27x3/2 power function: k = 27, p = 3/2
f (x) =5
9x2 =59
x−2 power function: k =59
, p = −2
![Page 33: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/33.jpg)
Which of the following functions are power functions of x?
f (x) = 2x4 power function: k = 2, p = 4
f (x) = x = 1x1 power function: k = 1, p = 1
f (x) =1x= 1x−1 power function: k = 1, p = −1
f (x) =5x3 = 5x−3 power function: k = 5, p = −3
f (x) = 2x not a power function
f (x) = 2x4 + 1 not a power function
f (x) = 3√
x = 3x1/2 power function: k = 3, p = 1/2
f (x) = (3√
x)3 = 27x3/2 power function: k = 27, p = 3/2
f (x) =5
9x2 =59
x−2 power function: k =59
, p = −2
![Page 34: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/34.jpg)
Which of the following functions are power functions of x?
f (x) = 2x4 power function: k = 2, p = 4
f (x) = x = 1x1 power function: k = 1, p = 1
f (x) =1x
= 1x−1 power function: k = 1, p = −1
f (x) =5x3 = 5x−3 power function: k = 5, p = −3
f (x) = 2x not a power function
f (x) = 2x4 + 1 not a power function
f (x) = 3√
x = 3x1/2 power function: k = 3, p = 1/2
f (x) = (3√
x)3 = 27x3/2 power function: k = 27, p = 3/2
f (x) =5
9x2 =59
x−2 power function: k =59
, p = −2
![Page 35: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/35.jpg)
Which of the following functions are power functions of x?
f (x) = 2x4 power function: k = 2, p = 4
f (x) = x = 1x1 power function: k = 1, p = 1
f (x) =1x= 1x−1 power function: k = 1, p = −1
f (x) =5x3 = 5x−3 power function: k = 5, p = −3
f (x) = 2x not a power function
f (x) = 2x4 + 1 not a power function
f (x) = 3√
x = 3x1/2 power function: k = 3, p = 1/2
f (x) = (3√
x)3 = 27x3/2 power function: k = 27, p = 3/2
f (x) =5
9x2 =59
x−2 power function: k =59
, p = −2
![Page 36: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/36.jpg)
Which of the following functions are power functions of x?
f (x) = 2x4 power function: k = 2, p = 4
f (x) = x = 1x1 power function: k = 1, p = 1
f (x) =1x= 1x−1 power function: k = 1, p = −1
f (x) =5x3
= 5x−3 power function: k = 5, p = −3
f (x) = 2x not a power function
f (x) = 2x4 + 1 not a power function
f (x) = 3√
x = 3x1/2 power function: k = 3, p = 1/2
f (x) = (3√
x)3 = 27x3/2 power function: k = 27, p = 3/2
f (x) =5
9x2 =59
x−2 power function: k =59
, p = −2
![Page 37: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/37.jpg)
Which of the following functions are power functions of x?
f (x) = 2x4 power function: k = 2, p = 4
f (x) = x = 1x1 power function: k = 1, p = 1
f (x) =1x= 1x−1 power function: k = 1, p = −1
f (x) =5x3 = 5x−3 power function: k = 5, p = −3
f (x) = 2x not a power function
f (x) = 2x4 + 1 not a power function
f (x) = 3√
x = 3x1/2 power function: k = 3, p = 1/2
f (x) = (3√
x)3 = 27x3/2 power function: k = 27, p = 3/2
f (x) =5
9x2 =59
x−2 power function: k =59
, p = −2
![Page 38: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/38.jpg)
Which of the following functions are power functions of x?
f (x) = 2x4 power function: k = 2, p = 4
f (x) = x = 1x1 power function: k = 1, p = 1
f (x) =1x= 1x−1 power function: k = 1, p = −1
f (x) =5x3 = 5x−3 power function: k = 5, p = −3
f (x) = 2x
not a power function
f (x) = 2x4 + 1 not a power function
f (x) = 3√
x = 3x1/2 power function: k = 3, p = 1/2
f (x) = (3√
x)3 = 27x3/2 power function: k = 27, p = 3/2
f (x) =5
9x2 =59
x−2 power function: k =59
, p = −2
![Page 39: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/39.jpg)
Which of the following functions are power functions of x?
f (x) = 2x4 power function: k = 2, p = 4
f (x) = x = 1x1 power function: k = 1, p = 1
f (x) =1x= 1x−1 power function: k = 1, p = −1
f (x) =5x3 = 5x−3 power function: k = 5, p = −3
f (x) = 2x not a power function
f (x) = 2x4 + 1 not a power function
f (x) = 3√
x = 3x1/2 power function: k = 3, p = 1/2
f (x) = (3√
x)3 = 27x3/2 power function: k = 27, p = 3/2
f (x) =5
9x2 =59
x−2 power function: k =59
, p = −2
![Page 40: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/40.jpg)
Which of the following functions are power functions of x?
f (x) = 2x4 power function: k = 2, p = 4
f (x) = x = 1x1 power function: k = 1, p = 1
f (x) =1x= 1x−1 power function: k = 1, p = −1
f (x) =5x3 = 5x−3 power function: k = 5, p = −3
f (x) = 2x not a power function
f (x) = 2x4 + 1
not a power function
f (x) = 3√
x = 3x1/2 power function: k = 3, p = 1/2
f (x) = (3√
x)3 = 27x3/2 power function: k = 27, p = 3/2
f (x) =5
9x2 =59
x−2 power function: k =59
, p = −2
![Page 41: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/41.jpg)
Which of the following functions are power functions of x?
f (x) = 2x4 power function: k = 2, p = 4
f (x) = x = 1x1 power function: k = 1, p = 1
f (x) =1x= 1x−1 power function: k = 1, p = −1
f (x) =5x3 = 5x−3 power function: k = 5, p = −3
f (x) = 2x not a power function
f (x) = 2x4 + 1 not a power function
f (x) = 3√
x = 3x1/2 power function: k = 3, p = 1/2
f (x) = (3√
x)3 = 27x3/2 power function: k = 27, p = 3/2
f (x) =5
9x2 =59
x−2 power function: k =59
, p = −2
![Page 42: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/42.jpg)
Which of the following functions are power functions of x?
f (x) = 2x4 power function: k = 2, p = 4
f (x) = x = 1x1 power function: k = 1, p = 1
f (x) =1x= 1x−1 power function: k = 1, p = −1
f (x) =5x3 = 5x−3 power function: k = 5, p = −3
f (x) = 2x not a power function
f (x) = 2x4 + 1 not a power function
f (x) = 3√
x
= 3x1/2 power function: k = 3, p = 1/2
f (x) = (3√
x)3 = 27x3/2 power function: k = 27, p = 3/2
f (x) =5
9x2 =59
x−2 power function: k =59
, p = −2
![Page 43: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/43.jpg)
Which of the following functions are power functions of x?
f (x) = 2x4 power function: k = 2, p = 4
f (x) = x = 1x1 power function: k = 1, p = 1
f (x) =1x= 1x−1 power function: k = 1, p = −1
f (x) =5x3 = 5x−3 power function: k = 5, p = −3
f (x) = 2x not a power function
f (x) = 2x4 + 1 not a power function
f (x) = 3√
x = 3x1/2 power function: k = 3, p = 1/2
f (x) = (3√
x)3 = 27x3/2 power function: k = 27, p = 3/2
f (x) =5
9x2 =59
x−2 power function: k =59
, p = −2
![Page 44: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/44.jpg)
Which of the following functions are power functions of x?
f (x) = 2x4 power function: k = 2, p = 4
f (x) = x = 1x1 power function: k = 1, p = 1
f (x) =1x= 1x−1 power function: k = 1, p = −1
f (x) =5x3 = 5x−3 power function: k = 5, p = −3
f (x) = 2x not a power function
f (x) = 2x4 + 1 not a power function
f (x) = 3√
x = 3x1/2 power function: k = 3, p = 1/2
f (x) = (3√
x)3
= 27x3/2 power function: k = 27, p = 3/2
f (x) =5
9x2 =59
x−2 power function: k =59
, p = −2
![Page 45: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/45.jpg)
Which of the following functions are power functions of x?
f (x) = 2x4 power function: k = 2, p = 4
f (x) = x = 1x1 power function: k = 1, p = 1
f (x) =1x= 1x−1 power function: k = 1, p = −1
f (x) =5x3 = 5x−3 power function: k = 5, p = −3
f (x) = 2x not a power function
f (x) = 2x4 + 1 not a power function
f (x) = 3√
x = 3x1/2 power function: k = 3, p = 1/2
f (x) = (3√
x)3 = 27x3/2 power function: k = 27, p = 3/2
f (x) =5
9x2 =59
x−2 power function: k =59
, p = −2
![Page 46: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/46.jpg)
Which of the following functions are power functions of x?
f (x) = 2x4 power function: k = 2, p = 4
f (x) = x = 1x1 power function: k = 1, p = 1
f (x) =1x= 1x−1 power function: k = 1, p = −1
f (x) =5x3 = 5x−3 power function: k = 5, p = −3
f (x) = 2x not a power function
f (x) = 2x4 + 1 not a power function
f (x) = 3√
x = 3x1/2 power function: k = 3, p = 1/2
f (x) = (3√
x)3 = 27x3/2 power function: k = 27, p = 3/2
f (x) =5
9x2
=59
x−2 power function: k =59
, p = −2
![Page 47: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/47.jpg)
Which of the following functions are power functions of x?
f (x) = 2x4 power function: k = 2, p = 4
f (x) = x = 1x1 power function: k = 1, p = 1
f (x) =1x= 1x−1 power function: k = 1, p = −1
f (x) =5x3 = 5x−3 power function: k = 5, p = −3
f (x) = 2x not a power function
f (x) = 2x4 + 1 not a power function
f (x) = 3√
x = 3x1/2 power function: k = 3, p = 1/2
f (x) = (3√
x)3 = 27x3/2 power function: k = 27, p = 3/2
f (x) =5
9x2 =59
x−2 power function: k =59
, p = −2
![Page 48: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/48.jpg)
Graph of Power Function
Blackboard
![Page 49: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/49.jpg)
Polynomials
DefinitionSums of power functions with non-negative integer exponentsare called polynomials.
Functions given by polynomials arecalled polynomial functions.Polynomial functions are of the form
f (x) = anxn + an−1xn−1 + · · ·+ a1x1 + a0
in which n is a non-negative integer, called degree and an is anon-zero number called leading coefficients.We call the term anxn the leading term.
![Page 50: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/50.jpg)
Polynomials
DefinitionSums of power functions with non-negative integer exponentsare called polynomials. Functions given by polynomials arecalled polynomial functions.
Polynomial functions are of the form
f (x) = anxn + an−1xn−1 + · · ·+ a1x1 + a0
in which n is a non-negative integer, called degree and an is anon-zero number called leading coefficients.We call the term anxn the leading term.
![Page 51: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/51.jpg)
Polynomials
DefinitionSums of power functions with non-negative integer exponentsare called polynomials. Functions given by polynomials arecalled polynomial functions.Polynomial functions are of the form
f (x) = anxn + an−1xn−1 + · · ·+ a1x1 + a0
in which n is a non-negative integer, called degree and an is anon-zero number called leading coefficients.We call the term anxn the leading term.
![Page 52: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/52.jpg)
Polynomials
DefinitionSums of power functions with non-negative integer exponentsare called polynomials. Functions given by polynomials arecalled polynomial functions.Polynomial functions are of the form
f (x) = anxn + an−1xn−1 + · · ·+ a1x1 + a0
in which n is a non-negative integer, called degree and an is anon-zero number called leading coefficients.
We call the term anxn the leading term.
![Page 53: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/53.jpg)
Polynomials
DefinitionSums of power functions with non-negative integer exponentsare called polynomials. Functions given by polynomials arecalled polynomial functions.Polynomial functions are of the form
f (x) = anxn + an−1xn−1 + · · ·+ a1x1 + a0
in which n is a non-negative integer, called degree and an is anon-zero number called leading coefficients.We call the term anxn the leading term.
![Page 54: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/54.jpg)
Polynomials of low degrees have special names:degree 1 linear
degree 2 quadraticdegree 3 cubicdegree 4 quarticdegree 5 quintic
The study of polynomial function and equations is almost asold as mathematics itself. The quadratic formula, for example,was found in some Babylonian clay tablets (around 2000BC).
![Page 55: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/55.jpg)
Polynomials of low degrees have special names:degree 1 lineardegree 2 quadratic
degree 3 cubicdegree 4 quarticdegree 5 quintic
The study of polynomial function and equations is almost asold as mathematics itself. The quadratic formula, for example,was found in some Babylonian clay tablets (around 2000BC).
![Page 56: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/56.jpg)
Polynomials of low degrees have special names:degree 1 lineardegree 2 quadraticdegree 3 cubic
degree 4 quarticdegree 5 quintic
The study of polynomial function and equations is almost asold as mathematics itself. The quadratic formula, for example,was found in some Babylonian clay tablets (around 2000BC).
![Page 57: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/57.jpg)
Polynomials of low degrees have special names:degree 1 lineardegree 2 quadraticdegree 3 cubicdegree 4 quartic
degree 5 quinticThe study of polynomial function and equations is almost asold as mathematics itself. The quadratic formula, for example,was found in some Babylonian clay tablets (around 2000BC).
![Page 58: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/58.jpg)
Polynomials of low degrees have special names:degree 1 lineardegree 2 quadraticdegree 3 cubicdegree 4 quarticdegree 5 quintic
The study of polynomial function and equations is almost asold as mathematics itself. The quadratic formula, for example,was found in some Babylonian clay tablets (around 2000BC).
![Page 59: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/59.jpg)
Polynomials of low degrees have special names:degree 1 lineardegree 2 quadraticdegree 3 cubicdegree 4 quarticdegree 5 quintic
The study of polynomial function and equations is almost asold as mathematics itself. The quadratic formula, for example,was found in some Babylonian clay tablets (around 2000BC).
![Page 60: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/60.jpg)
f (x) = anxn + an−1xn−1 + · · ·+ a1x1 + a0
ExampleWhich of the following functions are polynomial functions?
f (x) = 2x2 − 3x + 1 polynomial function: deg = 2, LC = 2f (x) = x polynomial function: deg = 1, LC = 1
f (x) = 2x−2 − 3x + 1 not a polynomial function
f (x) = 2x2 − 3x4 + 1 polynomial function: deg = 4, LC = −3
f (x) = x4 − 3x2 − x4 polynomial function: deg = 2, LC = −3f (x) = 2
√x − 3x + 1 not a polynomial function
f (x) = 5x7 polynomial function: deg = 7, LC = 5f (x) = 7 polynomial function: deg = 0, LC = 7
![Page 61: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/61.jpg)
f (x) = anxn + an−1xn−1 + · · ·+ a1x1 + a0
ExampleWhich of the following functions are polynomial functions?
f (x) = 2x2 − 3x + 1
polynomial function: deg = 2, LC = 2f (x) = x polynomial function: deg = 1, LC = 1
f (x) = 2x−2 − 3x + 1 not a polynomial function
f (x) = 2x2 − 3x4 + 1 polynomial function: deg = 4, LC = −3
f (x) = x4 − 3x2 − x4 polynomial function: deg = 2, LC = −3f (x) = 2
√x − 3x + 1 not a polynomial function
f (x) = 5x7 polynomial function: deg = 7, LC = 5f (x) = 7 polynomial function: deg = 0, LC = 7
![Page 62: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/62.jpg)
f (x) = anxn + an−1xn−1 + · · ·+ a1x1 + a0
ExampleWhich of the following functions are polynomial functions?
f (x) = 2x2 − 3x + 1 polynomial function: deg = 2, LC = 2
f (x) = x polynomial function: deg = 1, LC = 1
f (x) = 2x−2 − 3x + 1 not a polynomial function
f (x) = 2x2 − 3x4 + 1 polynomial function: deg = 4, LC = −3
f (x) = x4 − 3x2 − x4 polynomial function: deg = 2, LC = −3f (x) = 2
√x − 3x + 1 not a polynomial function
f (x) = 5x7 polynomial function: deg = 7, LC = 5f (x) = 7 polynomial function: deg = 0, LC = 7
![Page 63: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/63.jpg)
f (x) = anxn + an−1xn−1 + · · ·+ a1x1 + a0
ExampleWhich of the following functions are polynomial functions?
f (x) = 2x2 − 3x + 1 polynomial function: deg = 2, LC = 2f (x) = x
polynomial function: deg = 1, LC = 1
f (x) = 2x−2 − 3x + 1 not a polynomial function
f (x) = 2x2 − 3x4 + 1 polynomial function: deg = 4, LC = −3
f (x) = x4 − 3x2 − x4 polynomial function: deg = 2, LC = −3f (x) = 2
√x − 3x + 1 not a polynomial function
f (x) = 5x7 polynomial function: deg = 7, LC = 5f (x) = 7 polynomial function: deg = 0, LC = 7
![Page 64: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/64.jpg)
f (x) = anxn + an−1xn−1 + · · ·+ a1x1 + a0
ExampleWhich of the following functions are polynomial functions?
f (x) = 2x2 − 3x + 1 polynomial function: deg = 2, LC = 2f (x) = x polynomial function: deg = 1, LC = 1
f (x) = 2x−2 − 3x + 1 not a polynomial function
f (x) = 2x2 − 3x4 + 1 polynomial function: deg = 4, LC = −3
f (x) = x4 − 3x2 − x4 polynomial function: deg = 2, LC = −3f (x) = 2
√x − 3x + 1 not a polynomial function
f (x) = 5x7 polynomial function: deg = 7, LC = 5f (x) = 7 polynomial function: deg = 0, LC = 7
![Page 65: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/65.jpg)
f (x) = anxn + an−1xn−1 + · · ·+ a1x1 + a0
ExampleWhich of the following functions are polynomial functions?
f (x) = 2x2 − 3x + 1 polynomial function: deg = 2, LC = 2f (x) = x polynomial function: deg = 1, LC = 1
f (x) = 2x−2 − 3x + 1
not a polynomial function
f (x) = 2x2 − 3x4 + 1 polynomial function: deg = 4, LC = −3
f (x) = x4 − 3x2 − x4 polynomial function: deg = 2, LC = −3f (x) = 2
√x − 3x + 1 not a polynomial function
f (x) = 5x7 polynomial function: deg = 7, LC = 5f (x) = 7 polynomial function: deg = 0, LC = 7
![Page 66: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/66.jpg)
f (x) = anxn + an−1xn−1 + · · ·+ a1x1 + a0
ExampleWhich of the following functions are polynomial functions?
f (x) = 2x2 − 3x + 1 polynomial function: deg = 2, LC = 2f (x) = x polynomial function: deg = 1, LC = 1
f (x) = 2x−2 − 3x + 1 not a polynomial function
f (x) = 2x2 − 3x4 + 1 polynomial function: deg = 4, LC = −3
f (x) = x4 − 3x2 − x4 polynomial function: deg = 2, LC = −3f (x) = 2
√x − 3x + 1 not a polynomial function
f (x) = 5x7 polynomial function: deg = 7, LC = 5f (x) = 7 polynomial function: deg = 0, LC = 7
![Page 67: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/67.jpg)
f (x) = anxn + an−1xn−1 + · · ·+ a1x1 + a0
ExampleWhich of the following functions are polynomial functions?
f (x) = 2x2 − 3x + 1 polynomial function: deg = 2, LC = 2f (x) = x polynomial function: deg = 1, LC = 1
f (x) = 2x−2 − 3x + 1 not a polynomial function
f (x) = 2x2 − 3x4 + 1
polynomial function: deg = 4, LC = −3
f (x) = x4 − 3x2 − x4 polynomial function: deg = 2, LC = −3f (x) = 2
√x − 3x + 1 not a polynomial function
f (x) = 5x7 polynomial function: deg = 7, LC = 5f (x) = 7 polynomial function: deg = 0, LC = 7
![Page 68: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/68.jpg)
f (x) = anxn + an−1xn−1 + · · ·+ a1x1 + a0
ExampleWhich of the following functions are polynomial functions?
f (x) = 2x2 − 3x + 1 polynomial function: deg = 2, LC = 2f (x) = x polynomial function: deg = 1, LC = 1
f (x) = 2x−2 − 3x + 1 not a polynomial function
f (x) = 2x2 − 3x4 + 1 polynomial function: deg = 4, LC = −3
f (x) = x4 − 3x2 − x4 polynomial function: deg = 2, LC = −3f (x) = 2
√x − 3x + 1 not a polynomial function
f (x) = 5x7 polynomial function: deg = 7, LC = 5f (x) = 7 polynomial function: deg = 0, LC = 7
![Page 69: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/69.jpg)
f (x) = anxn + an−1xn−1 + · · ·+ a1x1 + a0
ExampleWhich of the following functions are polynomial functions?
f (x) = 2x2 − 3x + 1 polynomial function: deg = 2, LC = 2f (x) = x polynomial function: deg = 1, LC = 1
f (x) = 2x−2 − 3x + 1 not a polynomial function
f (x) = 2x2 − 3x4 + 1 polynomial function: deg = 4, LC = −3
f (x) = x4 − 3x2 − x4
polynomial function: deg = 2, LC = −3f (x) = 2
√x − 3x + 1 not a polynomial function
f (x) = 5x7 polynomial function: deg = 7, LC = 5f (x) = 7 polynomial function: deg = 0, LC = 7
![Page 70: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/70.jpg)
f (x) = anxn + an−1xn−1 + · · ·+ a1x1 + a0
ExampleWhich of the following functions are polynomial functions?
f (x) = 2x2 − 3x + 1 polynomial function: deg = 2, LC = 2f (x) = x polynomial function: deg = 1, LC = 1
f (x) = 2x−2 − 3x + 1 not a polynomial function
f (x) = 2x2 − 3x4 + 1 polynomial function: deg = 4, LC = −3
f (x) = x4 − 3x2 − x4 polynomial function: deg = 2, LC = −3
f (x) = 2√
x − 3x + 1 not a polynomial function
f (x) = 5x7 polynomial function: deg = 7, LC = 5f (x) = 7 polynomial function: deg = 0, LC = 7
![Page 71: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/71.jpg)
f (x) = anxn + an−1xn−1 + · · ·+ a1x1 + a0
ExampleWhich of the following functions are polynomial functions?
f (x) = 2x2 − 3x + 1 polynomial function: deg = 2, LC = 2f (x) = x polynomial function: deg = 1, LC = 1
f (x) = 2x−2 − 3x + 1 not a polynomial function
f (x) = 2x2 − 3x4 + 1 polynomial function: deg = 4, LC = −3
f (x) = x4 − 3x2 − x4 polynomial function: deg = 2, LC = −3f (x) = 2
√x − 3x + 1
not a polynomial function
f (x) = 5x7 polynomial function: deg = 7, LC = 5f (x) = 7 polynomial function: deg = 0, LC = 7
![Page 72: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/72.jpg)
f (x) = anxn + an−1xn−1 + · · ·+ a1x1 + a0
ExampleWhich of the following functions are polynomial functions?
f (x) = 2x2 − 3x + 1 polynomial function: deg = 2, LC = 2f (x) = x polynomial function: deg = 1, LC = 1
f (x) = 2x−2 − 3x + 1 not a polynomial function
f (x) = 2x2 − 3x4 + 1 polynomial function: deg = 4, LC = −3
f (x) = x4 − 3x2 − x4 polynomial function: deg = 2, LC = −3f (x) = 2
√x − 3x + 1 not a polynomial function
f (x) = 5x7 polynomial function: deg = 7, LC = 5f (x) = 7 polynomial function: deg = 0, LC = 7
![Page 73: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/73.jpg)
f (x) = anxn + an−1xn−1 + · · ·+ a1x1 + a0
ExampleWhich of the following functions are polynomial functions?
f (x) = 2x2 − 3x + 1 polynomial function: deg = 2, LC = 2f (x) = x polynomial function: deg = 1, LC = 1
f (x) = 2x−2 − 3x + 1 not a polynomial function
f (x) = 2x2 − 3x4 + 1 polynomial function: deg = 4, LC = −3
f (x) = x4 − 3x2 − x4 polynomial function: deg = 2, LC = −3f (x) = 2
√x − 3x + 1 not a polynomial function
f (x) = 5x7
polynomial function: deg = 7, LC = 5f (x) = 7 polynomial function: deg = 0, LC = 7
![Page 74: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/74.jpg)
f (x) = anxn + an−1xn−1 + · · ·+ a1x1 + a0
ExampleWhich of the following functions are polynomial functions?
f (x) = 2x2 − 3x + 1 polynomial function: deg = 2, LC = 2f (x) = x polynomial function: deg = 1, LC = 1
f (x) = 2x−2 − 3x + 1 not a polynomial function
f (x) = 2x2 − 3x4 + 1 polynomial function: deg = 4, LC = −3
f (x) = x4 − 3x2 − x4 polynomial function: deg = 2, LC = −3f (x) = 2
√x − 3x + 1 not a polynomial function
f (x) = 5x7 polynomial function: deg = 7, LC = 5
f (x) = 7 polynomial function: deg = 0, LC = 7
![Page 75: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/75.jpg)
f (x) = anxn + an−1xn−1 + · · ·+ a1x1 + a0
ExampleWhich of the following functions are polynomial functions?
f (x) = 2x2 − 3x + 1 polynomial function: deg = 2, LC = 2f (x) = x polynomial function: deg = 1, LC = 1
f (x) = 2x−2 − 3x + 1 not a polynomial function
f (x) = 2x2 − 3x4 + 1 polynomial function: deg = 4, LC = −3
f (x) = x4 − 3x2 − x4 polynomial function: deg = 2, LC = −3f (x) = 2
√x − 3x + 1 not a polynomial function
f (x) = 5x7 polynomial function: deg = 7, LC = 5f (x) = 7
polynomial function: deg = 0, LC = 7
![Page 76: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/76.jpg)
f (x) = anxn + an−1xn−1 + · · ·+ a1x1 + a0
ExampleWhich of the following functions are polynomial functions?
f (x) = 2x2 − 3x + 1 polynomial function: deg = 2, LC = 2f (x) = x polynomial function: deg = 1, LC = 1
f (x) = 2x−2 − 3x + 1 not a polynomial function
f (x) = 2x2 − 3x4 + 1 polynomial function: deg = 4, LC = −3
f (x) = x4 − 3x2 − x4 polynomial function: deg = 2, LC = −3f (x) = 2
√x − 3x + 1 not a polynomial function
f (x) = 5x7 polynomial function: deg = 7, LC = 5f (x) = 7 polynomial function: deg = 0, LC = 7
![Page 77: Section 1.9: Proportionality, Power Functions, And Polynomialstrchen.weebly.com/uploads/7/2/7/4/7274826/ch1-9.pdfSection 1.9: Proportionality, Power Functions, And Polynomials We have](https://reader030.vdocuments.mx/reader030/viewer/2022040822/5e6b7fc5e61a847aaa303a9d/html5/thumbnails/77.jpg)
End Behavior of Polynomial Functions
Blackboard