algebra 2 and trigonometry - white plains public schools...2 table of contents day 1: chapter...
TRANSCRIPT
![Page 1: Algebra 2 and Trigonometry - White Plains Public Schools...2 Table of Contents Day 1: Chapter 7-1/7-2: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Pgs](https://reader036.vdocuments.mx/reader036/viewer/2022071423/611e38cdd1de2b31544f2ab8/html5/thumbnails/1.jpg)
1
Algebra 2 and
Trigonometry
Chapter 7: Exponential Functions
Name:______________________________
Teacher:____________________________
Pd: _______
![Page 2: Algebra 2 and Trigonometry - White Plains Public Schools...2 Table of Contents Day 1: Chapter 7-1/7-2: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Pgs](https://reader036.vdocuments.mx/reader036/viewer/2022071423/611e38cdd1de2b31544f2ab8/html5/thumbnails/2.jpg)
2
Table of Contents
Day 1: Chapter 7-1/7-2: Laws of Exponents
SWBAT: Simplify positive, negative, and zero exponents. Pgs. 3 – 5 in Packet
HW: Page 289 #’s 3 – 25 odd
Pages 292 – 293 #’s 3 – 9 odd, 17, 18, 19, 22, 30, 32, 35 – 75 eoo
Day 2: Chapter 7-3: Rational Exponents
SWBAT: simplify rational exponents. Pgs. 6 – 10 in Packet
HW: Pages 296 – 298 #’s 3, 5, 6, 18, 19, 22, 32, 39 – 81 eoo
Day 3: Chapter 7-4: Exponential Functions
SWBAT: Graph Exponential Functions
Pgs. 11 – 15 in Packet
HW: Pages 302 – 303 #’s 3, 4, 7-9
QUIZ
Day 4: Chapter 7-5: Exponential Equations
SWBAT: Solve Exponential Equations
Pgs. 16 – 18 in Packet
HW: Page 305 #’s 1- 19 odd, 12, 23
Day 5: Chapter 7-6: Exponential Equations
SWBAT: Solve Exponential Equations with like and unlike bases
Pgs. 19 – 23 in Packet
HW: Pages 307- 308 #’s 3, 8, 9, 10, 15 – 35 odd
Day 6: Review
SWBAT: Solve Problems involving Exponents
Pgs. 24 – 27 in Packet
HW: Finish this section in the packet
HOMEWORK ANSWER KEYS – STARTS AT PAGE 28
![Page 3: Algebra 2 and Trigonometry - White Plains Public Schools...2 Table of Contents Day 1: Chapter 7-1/7-2: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Pgs](https://reader036.vdocuments.mx/reader036/viewer/2022071423/611e38cdd1de2b31544f2ab8/html5/thumbnails/3.jpg)
3
Day 1: Laws of Exponents
SWBAT: Simplify positive, negative, and zero exponents.
Warm – Up: Exponent Rules
Concept 1: Simplifying Exponents
LAWS of EXPONENTS: Test Question A. thru H.
#1. = ________ 1A. = ________
#2.
= ________ 2B. _______
5
12
x
x
#3. ( )y =
3C. ________43 x
#4. ( ) = _______ 4D. ( ) = _______
#5. (
)
= ________ 5E. (
)
= ________
Multiplication: Ex. x2 x
5 =
Division:
=
Ex.
=
Raising to a Power: (xa)b = x
ab Ex. (x
5)3
=
Power of a Product: (xy)a = x
a y
a Ex. ( )3 =
Power of a Quotient: a
aa
y
x
y
x
Ex. (
)
=
![Page 4: Algebra 2 and Trigonometry - White Plains Public Schools...2 Table of Contents Day 1: Chapter 7-1/7-2: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Pgs](https://reader036.vdocuments.mx/reader036/viewer/2022071423/611e38cdd1de2b31544f2ab8/html5/thumbnails/4.jpg)
4
Zero and Negative Exponents
LAWS of EXPONENTS: Test Questions
#6. 0;______0 xx 6F. = _______
( ) = _______ = _______
Ex. 1) Write 2
34
ab
bawith only positive exponents.
2) Write with only positive exponents.
3) Write the following with only positive exponents:
a) 52
23 )(
xy
y b)
4) Simplify each.
a) 57
34
3
6
yx
yx
b)
Zero exponents: 01 xx
x
xand
x
x nn
n
n
n
n
, so x
0 = 1
Negative Exponents: x- n
= nx
1 and (
)
= (
)
![Page 5: Algebra 2 and Trigonometry - White Plains Public Schools...2 Table of Contents Day 1: Chapter 7-1/7-2: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Pgs](https://reader036.vdocuments.mx/reader036/viewer/2022071423/611e38cdd1de2b31544f2ab8/html5/thumbnails/5.jpg)
5
Challenge Problem: Simplify. Use only positive exponents.
Summary/Closure:
Exit Ticket
![Page 6: Algebra 2 and Trigonometry - White Plains Public Schools...2 Table of Contents Day 1: Chapter 7-1/7-2: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Pgs](https://reader036.vdocuments.mx/reader036/viewer/2022071423/611e38cdd1de2b31544f2ab8/html5/thumbnails/6.jpg)
6
Day 2: Rational Exponents
SWBAT: Simplify rational exponents.
Warm - Up:
Rational Exponents
Exponential Form Radical Form
= ( √ )
Concept 1: Rewrite each in exponential form.
Teacher Modeled Student Try It!
(√ )
(√ )
root
power
xThink : = root powerx or
![Page 7: Algebra 2 and Trigonometry - White Plains Public Schools...2 Table of Contents Day 1: Chapter 7-1/7-2: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Pgs](https://reader036.vdocuments.mx/reader036/viewer/2022071423/611e38cdd1de2b31544f2ab8/html5/thumbnails/7.jpg)
7
Teacher Modeled Student Try It!
(√ )
(√ )
(√ )
(√ )
Concept 2: Rewrite each in radical form.
Teacher Modeled Student Try It!
![Page 8: Algebra 2 and Trigonometry - White Plains Public Schools...2 Table of Contents Day 1: Chapter 7-1/7-2: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Pgs](https://reader036.vdocuments.mx/reader036/viewer/2022071423/611e38cdd1de2b31544f2ab8/html5/thumbnails/8.jpg)
8
Use exponents to write the radical expression. Let the variable represent positive numbers.
Teacher Modeled Student Try It!
√
√
√
√
Write the given expression, using a radical sign. Let the variables represent positive numbers
Teacher Modeled Student Try It!
( )
![Page 9: Algebra 2 and Trigonometry - White Plains Public Schools...2 Table of Contents Day 1: Chapter 7-1/7-2: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Pgs](https://reader036.vdocuments.mx/reader036/viewer/2022071423/611e38cdd1de2b31544f2ab8/html5/thumbnails/9.jpg)
9
Practice:
1. If f(x) = 2
3
x , find f(16).
2. Evaluate
3.
![Page 10: Algebra 2 and Trigonometry - White Plains Public Schools...2 Table of Contents Day 1: Chapter 7-1/7-2: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Pgs](https://reader036.vdocuments.mx/reader036/viewer/2022071423/611e38cdd1de2b31544f2ab8/html5/thumbnails/10.jpg)
10
Challenge
Summary/Closure
Exit Ticket:
![Page 11: Algebra 2 and Trigonometry - White Plains Public Schools...2 Table of Contents Day 1: Chapter 7-1/7-2: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Pgs](https://reader036.vdocuments.mx/reader036/viewer/2022071423/611e38cdd1de2b31544f2ab8/html5/thumbnails/11.jpg)
11
Day 3 - Exponential Functions
SWBAT: Simplify rational exponents.
Warm - Up:
![Page 12: Algebra 2 and Trigonometry - White Plains Public Schools...2 Table of Contents Day 1: Chapter 7-1/7-2: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Pgs](https://reader036.vdocuments.mx/reader036/viewer/2022071423/611e38cdd1de2b31544f2ab8/html5/thumbnails/12.jpg)
12
An exponential function is of the form y = b 0, b 1, and x is a real number. Domain = {x∣x Real numbers}
Range = {y∣y }
Example 2: Graph y = (
)
, y = on the graph below.
Observations from above:
(1) (2) (3)
![Page 13: Algebra 2 and Trigonometry - White Plains Public Schools...2 Table of Contents Day 1: Chapter 7-1/7-2: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Pgs](https://reader036.vdocuments.mx/reader036/viewer/2022071423/611e38cdd1de2b31544f2ab8/html5/thumbnails/13.jpg)
13
Shifting the basic Exponential Graph f(x) =
Transformation Transformation up down left right Reflect over x-axis Reflect over y-axis
In examples 1 – 6, write an equation for each translation of y =
1. 2 units up __________________
2. 1 units down __________________
3. right 4 units __________________
4. left 3 units __________________
5. 1 units up, 4 units left __________________
6. 3 units down, 5 units right ________________
7. f(x) = means ________________
8. f(x) = (
)
means ________________
9. Graph f(x) = 10. Graph f(x) =
![Page 14: Algebra 2 and Trigonometry - White Plains Public Schools...2 Table of Contents Day 1: Chapter 7-1/7-2: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Pgs](https://reader036.vdocuments.mx/reader036/viewer/2022071423/611e38cdd1de2b31544f2ab8/html5/thumbnails/14.jpg)
14
Example 11
![Page 15: Algebra 2 and Trigonometry - White Plains Public Schools...2 Table of Contents Day 1: Chapter 7-1/7-2: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Pgs](https://reader036.vdocuments.mx/reader036/viewer/2022071423/611e38cdd1de2b31544f2ab8/html5/thumbnails/15.jpg)
15
Challenge
SUMMARY
Exit Ticket
![Page 16: Algebra 2 and Trigonometry - White Plains Public Schools...2 Table of Contents Day 1: Chapter 7-1/7-2: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Pgs](https://reader036.vdocuments.mx/reader036/viewer/2022071423/611e38cdd1de2b31544f2ab8/html5/thumbnails/16.jpg)
16
Day 4 - Exponential Equations
SWBAT: solve equations involving exponents.
Warm-Up: 1) What is the multiplicative inverse of ?3
2
2) What is the multiplicative inverse of ?3
1
_____________________________________________________________________________
To solve an equation involving exponents: Ex.
1. Write the equation with only the variable term 1.
on one side of the equation.
2. Divide both sides of the equation by the coefficient 2.
of the variable term.
3. Raise both sides of the equation to the power that is 3.
the reciprocal of the exponent of the variable.
4. Simplify the right side of the equation. 4.
5. Check the solution.
xxxx aa
aa
1
11
![Page 17: Algebra 2 and Trigonometry - White Plains Public Schools...2 Table of Contents Day 1: Chapter 7-1/7-2: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Pgs](https://reader036.vdocuments.mx/reader036/viewer/2022071423/611e38cdd1de2b31544f2ab8/html5/thumbnails/17.jpg)
17
Concept - Solve for x in each exponential equation:
Teacher Modeled Student Try It!
√
√
![Page 18: Algebra 2 and Trigonometry - White Plains Public Schools...2 Table of Contents Day 1: Chapter 7-1/7-2: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Pgs](https://reader036.vdocuments.mx/reader036/viewer/2022071423/611e38cdd1de2b31544f2ab8/html5/thumbnails/18.jpg)
18
Challenge
Summary/Closure
Exit Ticket:
![Page 19: Algebra 2 and Trigonometry - White Plains Public Schools...2 Table of Contents Day 1: Chapter 7-1/7-2: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Pgs](https://reader036.vdocuments.mx/reader036/viewer/2022071423/611e38cdd1de2b31544f2ab8/html5/thumbnails/19.jpg)
19
Day 5 - Exponential Equations involving like/unlike bases
SWBAT: Solve Exponential Equations with like and unlike bases
Warm-Up:
1) Express 36 as a power.
2) Express 81 as a power.
3) Express 32 as a power.
Concept 1: Solving Exponential Equations with the like Bases
If the bases are equal, the exponents must be equal.
Ex. Solve for x: 3x = 3
2x-2
To solve an equation with like bases: Ex.
1. Write the equation. 1.
2. Since the bases are alike, equate the exponents. 2.
3. Solve the resulting equation. 3.
![Page 20: Algebra 2 and Trigonometry - White Plains Public Schools...2 Table of Contents Day 1: Chapter 7-1/7-2: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Pgs](https://reader036.vdocuments.mx/reader036/viewer/2022071423/611e38cdd1de2b31544f2ab8/html5/thumbnails/20.jpg)
20
Concept 1 - Solving Exponential Equations with the like Bases
Teacher Modeled Student Try It!
(
)
(
)
Concept 2: Solving Exponential Equations with Different Bases
If possible, write each term as a power of the same base.
Solve for x and check: 22x
= 8
To solve an equation with unlike bases: Ex.
1. Write the equation. 1.
2. Change the “higher” base to a power of the smaller base. 2.
3. Simplify the “higher” base. 3.
4. Since the bases are alike, equate the exponents. 5.
5. Solve the resulting equation. 5.
![Page 21: Algebra 2 and Trigonometry - White Plains Public Schools...2 Table of Contents Day 1: Chapter 7-1/7-2: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Pgs](https://reader036.vdocuments.mx/reader036/viewer/2022071423/611e38cdd1de2b31544f2ab8/html5/thumbnails/21.jpg)
21
Concept 2 - Solving Exponential Equations with the unlike Bases
Teacher Modeled Student Try It!
Concept 3: Solving Exponential Equations with Different Bases (neither base is the power of
the other)
If possible, write each term as a power of the same base.
Solve for x and check: 9x+1
= 27x
To solve an equation with unlike bases: Ex.
1. Write the equation. 1.
2. Change each base to a power of the same number. 2.
3. Simplify each base. 3.
4. Since the bases are alike, equate the exponents. 5.
5. Solve the resulting equation. 5.
![Page 22: Algebra 2 and Trigonometry - White Plains Public Schools...2 Table of Contents Day 1: Chapter 7-1/7-2: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Pgs](https://reader036.vdocuments.mx/reader036/viewer/2022071423/611e38cdd1de2b31544f2ab8/html5/thumbnails/22.jpg)
22
Concept 3 - Solving Exponential Equations with the unlike Bases(neither base is the power of
the other)
Teacher Modeled Student Try It!
5x-1 = (0.04)2x (
)
![Page 23: Algebra 2 and Trigonometry - White Plains Public Schools...2 Table of Contents Day 1: Chapter 7-1/7-2: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Pgs](https://reader036.vdocuments.mx/reader036/viewer/2022071423/611e38cdd1de2b31544f2ab8/html5/thumbnails/23.jpg)
23
Challenge
Summary/Closure
Exit Ticket
![Page 24: Algebra 2 and Trigonometry - White Plains Public Schools...2 Table of Contents Day 1: Chapter 7-1/7-2: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Pgs](https://reader036.vdocuments.mx/reader036/viewer/2022071423/611e38cdd1de2b31544f2ab8/html5/thumbnails/24.jpg)
24
Day 6 – Review of Exponential Functions
![Page 25: Algebra 2 and Trigonometry - White Plains Public Schools...2 Table of Contents Day 1: Chapter 7-1/7-2: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Pgs](https://reader036.vdocuments.mx/reader036/viewer/2022071423/611e38cdd1de2b31544f2ab8/html5/thumbnails/25.jpg)
25
c.
d.
![Page 26: Algebra 2 and Trigonometry - White Plains Public Schools...2 Table of Contents Day 1: Chapter 7-1/7-2: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Pgs](https://reader036.vdocuments.mx/reader036/viewer/2022071423/611e38cdd1de2b31544f2ab8/html5/thumbnails/26.jpg)
26
![Page 27: Algebra 2 and Trigonometry - White Plains Public Schools...2 Table of Contents Day 1: Chapter 7-1/7-2: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Pgs](https://reader036.vdocuments.mx/reader036/viewer/2022071423/611e38cdd1de2b31544f2ab8/html5/thumbnails/27.jpg)
27
48. Explain each transformation below from y = .
a) y = ________________
b) y = ________________
c) y = ________________
d) y = ________________
e) y = ________________
f) y = (
)
________________
![Page 28: Algebra 2 and Trigonometry - White Plains Public Schools...2 Table of Contents Day 1: Chapter 7-1/7-2: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Pgs](https://reader036.vdocuments.mx/reader036/viewer/2022071423/611e38cdd1de2b31544f2ab8/html5/thumbnails/28.jpg)
28
HW ANSWERS
![Page 29: Algebra 2 and Trigonometry - White Plains Public Schools...2 Table of Contents Day 1: Chapter 7-1/7-2: Laws of Exponents SWBAT: Simplify positive, negative, and zero exponents. Pgs](https://reader036.vdocuments.mx/reader036/viewer/2022071423/611e38cdd1de2b31544f2ab8/html5/thumbnails/29.jpg)
29
Day 6 - REVIEW
c. d. y = (
)
48a. shift 2 right 48b. shift 2 down 48c. shift 4 right, up 7 48d. shift 1 left, down 8 48e. reflect over x-axis, up 1 48f. reflect y = 3-x over y-axis, shift 6 right