PMI Unit 2 Working With Functions NJCTL.org

Vertical Shifts

Class Work

Part 1: In each question below, g(x) is shown. Re-graph g(x) using the transformation indicated.

1. a) 2. a)

b) b)

Part 2: In each exercise the function h(x) is given. (i) Identify its parent function, (ii) describe the transformation(s) needed to go from the parent function to h(x), (iii) draw the graph of both on one graph.

PMI Unit 2 Working With Functions NJCTL.org

1. i)

ii) Move down 2

iii)

1. i)

ii) Move up 3

iii)

1. i)

ii) Move up 1

iii)

1. i)

ii) Move down 1

iii)

1. i)

ii) Move down 4

iii)

PMI Unit 2 Working With Functions NJCTL.org

Vertical Shifts

Homework

Part 1: In each question below, g(x) is shown. Re-graph g(x) using the transformation indicated.

8. a) 9. a)

b) b)

Part 2: In each exercise the function h(x) is given. (i) Identify its parent function, (ii) describe the transformation(s) needed to go from the parent function to h(x), (iii) draw the graph of both on one graph.

PMI Unit 2 Working With Functions NJCTL.org

1. i)

ii) Move up 3

iii)

1. i)

ii) Move down 2

iii)

1. i)

ii) Move up 2

iii)

1. i)

ii) Move up 3

iii)

1. i)

ii) Move down 4

iii)

PMI Unit 2 Working With Functions NJCTL.org

Spiral Review

15.(2x + 3)(x – 1)16.17. x3 – 3x2 +5x – 318. 4x2 + 12x + 9

Horizontal Shifts

Class Work

Part 1: In each question below, g(x) is shown. Re-graph g(x) using the transformation indicated.

19. a) 20. a)

b) b)

Part 2: In each exercise the function h(x) is given. (i) Identify its parent function, (ii) describe the transformation(s) needed to go from the parent function to h(x), (iii) draw the graph of both on one graph.

PMI Unit 2 Working With Functions NJCTL.org

1. i)

ii) Move right 2

iii)

1. i)

ii) Move left 3

iii)

1. i)

ii) Move left 1

iii)

1. i)

ii) Move right 1

iii)

1. i)

ii) Move right 4

iii)

PMI Unit 2 Working With Functions NJCTL.org

Horizontal Shifts

Homework

Part 1: In each question below, g(x) is shown. Re-graph g(x) using the transformation indicated.

26. a) 27. a)

b) b)

Part 2: In each exercise the function h(x) is given. (i) Identify its parent function, (ii) describe the transformation(s) needed to go from the parent function to h(x), (iii) draw the graph of both on one graph.

PMI Unit 2 Working With Functions NJCTL.org

28. i)

ii) Move right 3

iii)

1. i)

ii) Move right 2

iii)

1. i)

ii) Move left 4

iii)

1. i)

ii) Move right 5

iii)

1. i)

ii) Move right 2

iii)

PMI Unit 2 Working With Functions NJCTL.org

Spiral Review

33. x3 – 3x2 + 3x +134.(2x – 5)(3x – 2)35.36.

Reflections

Class Work

Part 1: In each question below, g(x) is shown. Re-graph g(x) using the transformation indicated.

37. a) 38. a)

b) b)

Part 2: In each exercise the function h(x) is given. (i) Identify its parent function, (ii) describe the transformation(s) needed to go from the parent function to h(x), (iii) draw the graph of both on one graph.

PMI Unit 2 Working With Functions NJCTL.org

1. i)

ii) Reflect over x-axis

iii)

1. i)

ii) Reflect over y-axis

iii)

1. i)

ii) Reflect over y-axis

iii)

1. i)

ii) Reflect over x-axis

iii)

1. i)

ii) Reflect over y-axis

iii)

PMI Unit 2 Working With Functions NJCTL.org

Reflections

Homework

Part 1: In each question below, g(x) is shown. Re-graph g(x) using the transformation indicated.

44. a) 45. a)

b) b)

Part 2: In each exercise the function h(x) is given. (i) Identify its parent function, (ii) describe the transformation(s) needed to go from the parent function to h(x), (iii) draw the graph of both on one graph.

PMI Unit 2 Working With Functions NJCTL.org

1. i)

ii) Reflect over y-axis

iii)

1. i)

ii) Reflect over x-axis

iii)

1. i)

ii) Reflect over x-axis

iii)

1. i)

ii) Reflect over x-axis

iii)

1. i)

ii) Reflect over x-axis

iii)

PMI Unit 2 Working With Functions NJCTL.org

Spiral Review

51.52. 8x3 +12x2 + 6x + 153. 3x3 +11x2 – 454.

Vertical Stretches and Shrinks

Class Work

Part 1: In each question below, g(x) is shown. Re-graph g(x) using the transformation indicated.

55. a) 56. a)

b) b)

Part 2: In each exercise the function h(x) is given. (i) Identify its parent function, (ii) describe the transformation(s) needed to go from the parent function to h(x), (iii) draw the graph of both on one graph.

PMI Unit 2 Working With Functions NJCTL.org

1. i)

ii) Vertical stretch of 2

iii)

1. i)

ii) Vertical stretch of 3

iii)

1. i)

ii) Vertical shrink of

iii)

1. i)

ii) Vertical shrink of

iii)

1. i)

ii) Vertical stretch of 3

iii)

PMI Unit 2 Working With Functions NJCTL.org

Vertical Stretches and Shrinks

Homework

Part 1: In each question below, g(x) is shown. Re-graph g(x) using the transformation indicated.

62. a) 63. a)

b) b)

Part 2: In each exercise the function h(x) is given. (i) Identify its parent function, (ii) describe the transformation(s) needed to go from the parent function to h(x), (iii) draw the graph of both on one graph.

PMI Unit 2 Working With Functions NJCTL.org

1. i)

ii) Vertical stretch of 4

iii)

1. i)

ii) Vertical shrink of 0.25

iii)

1. i)

ii) Vertical shrink of

iii)

1. i)

ii) Vertical stretch of 3

iii)

1. i)

ii) Vertical shrink of

iii)

PMI Unit 2 Working With Functions NJCTL.org

Spiral Review

69.70. -3771. 27x3 + 54x2 +36x + 872.

Horizontal Stretches and Shrinks

Class Work

Part 1: In each question below, g(x) is shown. Re-graph g(x) using the transformation indicated.

73. a) 74. a)

b) b)

Part 2: In each exercise the function h(x) is given. (i) Identify its parent function, (ii) describe the transformation(s) needed to go from the parent function to h(x), (iii) draw the graph of both on one graph.

PMI Unit 2 Working With Functions NJCTL.org

1. i)

ii) Horizontal shrink of 2

iii)

1. i)

ii) Horizontal shrink of 3

iii)

1. i)

ii) Horizontal stretch of

iii)

1. i)

ii) Horizontal stretch of

iii)

1. i)

ii) Horizontal shrink of 3

iii)

PMI Unit 2 Working With Functions NJCTL.org

Horizontal Stretches and Shrinks

Homework

Part 1: In each question below, g(x) is shown. Re-graph g(x) using the transformation indicated.

80. a) 81. a)

b) b)

Part 2: In each exercise the function h(x) is given. (i) Identify its parent function, (ii) describe the transformation(s) needed to go from the parent function to h(x), (iii) draw the graph of both on one graph.

PMI Unit 2 Working With Functions NJCTL.org

1. i)

ii) Horizontal shrink of 4

iii)

1. i)

ii) Horizontal stretch of .25

iii)

1. i)

ii) Horizontal stretch of

iii)

1. i)

ii) Horizontal shrink of 2

iii)

1. i)

ii) Horizontal stretch of

iii)

PMI Unit 2 Working With Functions NJCTL.org

Spiral Review

87. x2 + 10x +2588. (3x + 5)(3x – 5)89. Unfactorable90. -12x7 – 15x5

Combining Transformations

Class Work

Part 1: In each question below, g(x) is shown. Re-graph g(x) using the transformation indicated.

91. a) 92. a)

b) b)

Part 2: In each exercise the function h(x) is given. (i) Identify its parent function, (ii) describe the transformation(s) needed to go from the parent function to h(x), (iii) draw the graph of both on one graph.

PMI Unit 2 Working With Functions NJCTL.org

1. i)

ii) Reflect over y-axis, move right 3, vertical stretch of 4, move up 6

iii)

1. i)

ii) Horizontal shrink of 2, move left 1, vertical stretch of 3, move down 2

iii)

1. i)

ii) Reflect over y-axis, move right 3,vertical stretch of 2, move up 4

iii)

1. i)

ii) Horizontal shrink of 3, move right 2, vertical stretch of 2, move down 1

iii)

1. i)

ii) Horizontal shrink of 2, reflect over y-axis, vertical stretch of 3, move up 4

iii)

PMI Unit 2 Working With Functions NJCTL.org

Combining Transformations

Homework

Part 1: In each question below, g(x) is shown. Re-graph g(x) using the transformation indicated.

98. a) 99. a)

b) b)

Part 2: In each exercise the function h(x) is given. (i) Identify its parent function, (ii) describe the transformation(s) needed to go from the parent function to h(x), (iii) draw the graph of both on one graph.

PMI Unit 2 Working With Functions NJCTL.org

1. i)

ii) Horizontal shrink of 2, move right 3, vertical stretch of 4, move up 2

iii)

1. i)

ii) Move right 2, vertical stretch of 3, move down 4

iii)

1. i)

ii) Horizontal stretch of , move right 6, reflect over x-axis

iii)

1. i)

ii) Reflect over y-axis, move down 3

iii)

1. i)

ii) Reflect over y-axis, move right 2, move up 4

iii)

PMI Unit 2 Working With Functions NJCTL.org

Spiral Review

105. 9x2 – 24x + 16106.107. (5x + 1)(5x – 1) 108. Unfactorable

Operations with Functions

Class Work

109. a)

b) 11

c) -3

d) 15

110. a)

b) 24

c) -4

d) 56

111. a)

b) 2

c) -4

d) 1

1. a)

b) 7

c) -11

d) -5

1. a)

b)

c) -4

d)

Spiral Review

114.115. 116. (4x + 9)(4x – 9)117. 8x3 + 12x2 + 4x + 6

Operations with Functions

Homework

1. a)

b) -6.55

c) 1

d) -78

1. a)

b) 2.45

c) -2

d) 12

1. a)

b) 3.67

c)

d) 27

1. a)

b) 40.1

c) 1

d) 399

1. a)

b) -.03

c) -2

d)

Spiral Review

123.124.125.

Composite Functions

Class Work

1. a)

b) -2

1. a)

b) 82

1. a)

b)

1. a)

b)

1. a)

b) 1

Spiral Review

131.132. 133.134. 16m7n7

Composite Functions

Homework

1. a)

b) 6

1. a)

b) 93

1. a)

b)

1. a)

b) 3

1. a)

b) -3

Spiral Review

140.141.142.

Inverse Functions

Class Work

PMI Unit 2 Working With Functions NJCTL.org

1. i)

ii)

iii) D: all reals

R: all reals

1. i)

ii)

iii) D:

R: all reals

1. i)

ii)

iii) D:

R: all real numbers

1. i)

ii)

iii) D:

R:

1. i)

ii)

iii) D: all reals

R:

PMI Unit 2 Working With Functions NJCTL.org

Spiral Review

148.149. (4x – 5y)(4x + 5y)150.16x12y8151. H. shrink 3, reflect y, 2

Inverse Functions

Homework

PMI Unit 2 Working With Functions NJCTL.org

1. i)

ii)

iii) D: all reals

R: all reals

1. i)

ii)

iii) D:

R: all reals

1. i)

ii)

iii) D: all reals

R:

1. i)

ii)

iii) D:

R:

1. i)

ii)

iii) D: all reals

R:

PMI Unit 2 Working With Functions NJCTL.org

Spiral Review

157.158.(8x – 1)(2x + 3)159. -27x6y12160. 2, v. stretch 2, reflect x, 5

Piecewise Functions

Class Work

161. a. f(-2) = 465
b. f(1) = 8
c. f(4) = 74
d. D: all reals
R:
e.
162. a. f(-2) = -10
b. f(0) = 2
c. f(4) = 4
d. D: all reals
R:
e. / 163. a. f(-5) = -1
b. f(0) = -4
c. f(4) = 6
d. D: all reals
R:
e.
164. b = -3

Piecewise Functions

Homework

165. a. f(-2) = -2
b. f(0) = 6
c. f(3) = -3
d. D: all reals
R:
e.
166. a. f(-2) =
b. f(0) = 0
c. f(4) =
d. D: all reals
R: all reals
e. / 167. a. f(-5) = -2
b. f(0) = -4
c. f(4) = 1
d. D: all reals
R:
e.
168. a = -1.2 b = -3.6

Spiral Review

169.170. (9x + 4y)(9x – 4y)171. -8x7y6172. 2, reflect x, 5

PMI Unit 2 Working With Functions NJCTL.org

Unit Review Questions

Multiple Choice

1. Describe the transformation of the parent function f(x) = x2 to g(x) = x2 – 1
2. shift left 1
3. shift right 1
4. shift down 1
5. shift up 1
6. Describe the transformation of the parent function f(x) = |x| to g(x) = | x+1|
7. shift left 1
8. shift right 1
9. shift down 1
10. shift up 1
1. Describe the transformation of the parent function f(x)= [x] to g(x)= [2x]
2. horizontal stretch of scale factor 2
3. horizontal stretch of scale factor 1/2
4. vertical stretch of scale factor 2
5. vertical stretch of scale factor 1/2
1. Describe the transformation of the parent function f(x)= to g(x)=
2. horizontal stretch of scale factor 2
3. horizontal stretch of scale factor 1/2
4. vertical stretch of scale factor 2
5. vertical stretch of scale factor ½
1. Describe the transformation of the parent function f(x)= log(x) to g(x)= log(-x)
2. horizontal reflection
3. vertical reflection
4. does not affect f(x) since it is symmetrical
5. not possible because log(x) is undefined for negatives
1. The order of the following transformation of to is
2. Slide 3 right, stretch 4 vertically, slide 5 up
3. Slide 3 left, stretch 4 vertically, slide 5 up
4. Reflect over the y-axis, slide 3 right, stretch 4 vertically, slide 5 up
5. Reflect over the y-axis, slide 3 left, stretch 4 vertically, slide 5 up
1. , , and h(3)=
2. 78
3. 26
4. 24
5. 18
6. , , and h(3)=
7. -50
8. -25
9. 25
10. -12.5
11. , , and h(3)=
12. -539
13. -38.5
14. -7
15. 7
1. , , and h(3)=
2. -5
3. -3
4. -1
5. 1
1. , , and h(2a+1)=
1. Given , find
2. -1022
3. 2
1. Given and , find a.
2. -27
3. -56
1. , find a(3).
2. 5
3. -10
4. 5 or -10
5. Undefined
1. , find such that b(x) is continuous
2. -8
3. -4
4. 4
5. 8

Unit Review Questions

Extended Response

1. Given the function of f(x) as shown at the right
1. m=3,-2
2. For which value of m is the rate of change about h(3) the closest?
3. Find h(3) in terms of m.
1. Given , describe the type and locations of any discontinuities of f(x)
2. Vertical Asymptote at x=-2.5, Horizontal Asymptote at y=0
3. Vertical Asymptote at x=0, Horizontal Asymptote at y=1
4. Vertical Asymptote at x=-2, Horizontal Asymptote at y=0
5. Write a piecewise function f(x) so that the hole in g(x) is removed.
1. People enter a park at a rate of where t is the number of hours after opening.

People leave the park at a rate of . The park is open 12 hours a day.

1. Write an, P(t) equation for the rate of change in the number of people in the park in terms of E(t) and L(t).
2. Create the piecewise function for P(t).
3. Find c so that there is no one in the park at closing.
4. Does the answer in part c make sense? Explain.