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