warm–up #3. warm–up #3 solutions homework log tues 11/3 lesson 3 – 2 learning objective: to...
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Warm–up #31. Find domain & range
2. g(x) = , find g(x + h)
Warm–up #3 Solutions1. Find domain & range Domain: Range: [0, )2. g(x) = , find g(x + h)=
=
Homework LogTues
11/3
Lesson 3 – 2
Learning Objective: To find difference quotients & to graph functions
Hw: #304 Pg. 179 #45 – 51 odd, 54, 56, 57 – 63 odd, 64, 70 – 76 even
11/3/15 Lesson 3 – 2 Difference Quotients & Function Graphs Day 2
Advanced Math/Trig
Learning Objective
To find difference quotient
To evaluate functions
To graph absolute value and quadratic functions
To graph step functions
Difference QuotientUsed in Calculus to study tangent lines to curves
Find the Difference Quotient
1.
=
=
=
= =
Find the Difference Quotient
2. f(x) = 4x – 5
=
=
=
Find the Difference Quotient
3.
=
=
Find the Difference Quotient
3.
=
=
=
=
Function4. Determine if this is a function
No! It doesn’t pass the vertical line test.
Function GraphsAbsolute Value FunctionsVertex (h, k)
Quadratic Functions
To find the x value of the vertexx =
Plug back into original function to find y
5.
Vertex: (0, –4)
x y
V(0 – 4)
– 2– 1
1 2
– 2 – 3
– 3 – 2
Is a function.
Passes the vertical line test.
6. Vertex: (3, 0)
x y
V(3 0)
1 2
4 5
2 1
1 2
Is a function.
Passes the vertical line test.
7. Vertex: (–2, 3)
x y
V(– 2 3)
– 4 – 3
– 1 0
5 4
4 5
Is a function.
Passes the vertical line test.
8. Vertex: (0, 1)
x y
V(0 1)
– 2 – 1
1 2
5 2
2 5
x = = 0
y =
Is a function.
Passes the vertical line test.
9.
Vertex: (1, –5)
x y
V( 1 –5)
– 1 0
2 3
3 –3
–3 3
x = = 1
y =
Is a function.
Passes the vertical line test.
Greatest Integer Function
Greatest Integer x
1.
2.
3.
4.
5.
6.
7.
8.
–4 –3 –2 –1 0 1 2 3 4 5 6 7
= 5
= 0
Graph 9. Plug in positive decimal values 1 to get a pattern and then fill in the negatives.
1.01.21.92.02.22.93.0
x y
1112223
y
x
Is a function, so must pass the vertical line test.
Greatest Integer Function
9.
y
x
0 1x 1 2x 2 3x
1 0x 012
1
Actual Table: x y
y
x
Graph 10.
1.01.21.92.02.22.93.0
x y
3334445
y
x
Graph 11.
1.01.21.92.02.22.93.0
x y
–2–2–2–1–1–10
Evaluate 12.
Find f (1.3)
Plug into calculator!
= – 4.283
Evaluate the difference quotient
13. x = 4 and h = 0.02
=
Plug into calculator!
= 1.02
Ticket Out the Door
Find the difference quotient
f(x) =
Homework
#304 Pg. 179 #45 – 51 odd, 54, 56, 57 – 63 odd, 64, 70 – 76 even