1. g(x) = -x + 2 2. g(x) = x 2 – 2 3. g(x)= 2 – 0.2x 4. g(x) = 2|x| – 2 5. g(x) = 2.2(x+ 2) 2 Algebra II 1

1. g(x) = -x + 2 2. g(x) = x 2 2 3. g(x)= 2 0.2x 4. g(x) = 2|x| 2 5. g(x) = 2.2(x+ 2) 2 Algebra II 1

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1. g(x) = -x + 22. g(x) = x2 – 2 3. g(x)= 2 – 0.2x4. g(x) = 2|x| – 2 5. g(x) = 2.2(x+ 2)2

Algebra II 1

Algebra II

Transformations of Linear and Absolute Value Functions

3Algebra II

Page 4: 1. g(x) = -x + 2 2. g(x) = x 2 2 3. g(x)= 2 0.2x 4. g(x) = 2|x| 2 5. g(x) = 2.2(x+ 2) 2 Algebra II 1

4Algebra II

Page 5: 1. g(x) = -x + 2 2. g(x) = x 2 2 3. g(x)= 2 0.2x 4. g(x) = 2|x| 2 5. g(x) = 2.2(x+ 2) 2 Algebra II 1

5Algebra II

Page 6: 1. g(x) = -x + 2 2. g(x) = x 2 2 3. g(x)= 2 0.2x 4. g(x) = 2|x| 2 5. g(x) = 2.2(x+ 2) 2 Algebra II 1

6Algebra II

Page 7: 1. g(x) = -x + 2 2. g(x) = x 2 2 3. g(x)= 2 0.2x 4. g(x) = 2|x| 2 5. g(x) = 2.2(x+ 2) 2 Algebra II 1

7Algebra II

Page 8: 1. g(x) = -x + 2 2. g(x) = x 2 2 3. g(x)= 2 0.2x 4. g(x) = 2|x| 2 5. g(x) = 2.2(x+ 2) 2 Algebra II 1

8Algebra II

Page 9: 1. g(x) = -x + 2 2. g(x) = x 2 2 3. g(x)= 2 0.2x 4. g(x) = 2|x| 2 5. g(x) = 2.2(x+ 2) 2 Algebra II 1

9Algebra II

1. f(x) = |1/3 x| ; translation 2 units left.

2. f(x) = -|x+9| -1; translation 6 units down.

3. f(x) = -2x + 2; translation 7 units down

Page 10: 1. g(x) = -x + 2 2. g(x) = x 2 2 3. g(x)= 2 0.2x 4. g(x) = 2|x| 2 5. g(x) = 2.2(x+ 2) 2 Algebra II 1

10Algebra II

4. f(x) = 1/2x + 8 ; reflection in the x axis.

5. f(x) = 4 + |x + 1|; reflection in the y axis.

6. f(x) = -5x; vertical shrink by factor of 1/5

Page 11: 1. g(x) = -x + 2 2. g(x) = x 2 2 3. g(x)= 2 0.2x 4. g(x) = 2|x| 2 5. g(x) = 2.2(x+ 2) 2 Algebra II 1

11Algebra II

7. f(x) = |x +3|+2 ; vertical stretch by factor 4

8. f(x) = 3x – 9; horizontal stretch by a factor of 6

9. f(x) = -|8x| - 4; horizontal shrink by a factor of ¼

Page 12: 1. g(x) = -x + 2 2. g(x) = x 2 2 3. g(x)= 2 0.2x 4. g(x) = 2|x| 2 5. g(x) = 2.2(x+ 2) 2 Algebra II 1

Algebra II 12

10. Consider the function f(x) = |x|. Write a function g whose graph represents a reflection in the x- axis followed by a horizontal stretch by a factor of 3 and a translation 5 units down. 11. Which of the transformation(s) will not change

the y-intercept of f(x) = |x | + 3?

Page 13: 1. g(x) = -x + 2 2. g(x) = x 2 2 3. g(x)= 2 0.2x 4. g(x) = 2|x| 2 5. g(x) = 2.2(x+ 2) 2 Algebra II 1

a. Write a function g whose graph is a translation 3 units down of the graph of f.

a. Write a function h whose graph is a translation 2 units to the left of the graph of f.

Algebra II 13

Page 14: 1. g(x) = -x + 2 2. g(x) = x 2 2 3. g(x)= 2 0.2x 4. g(x) = 2|x| 2 5. g(x) = 2.2(x+ 2) 2 Algebra II 1

14Algebra II

a. Write a function g whose graph is a translation 5 units up of the graph of f.

a. Write a function h whose graph is a translation 1 unit to the right of the graph of f.

Page 15: 1. g(x) = -x + 2 2. g(x) = x 2 2 3. g(x)= 2 0.2x 4. g(x) = 2|x| 2 5. g(x) = 2.2(x+ 2) 2 Algebra II 1

Algebra II 15

a. Write a function g whose graph is a reflection in the x axis of the graph f.

a. Write a function h whose graph is a reflection in the y-axis of the graph of f.

Page 16: 1. g(x) = -x + 2 2. g(x) = x 2 2 3. g(x)= 2 0.2x 4. g(x) = 2|x| 2 5. g(x) = 2.2(x+ 2) 2 Algebra II 1

Algebra II 16

a. Write a function h whose graph is a reflection in the x-axis of the graph of f.

a. Write a function g whose graph is a translation in the y-axis of the graph of f.

Page 17: 1. g(x) = -x + 2 2. g(x) = x 2 2 3. g(x)= 2 0.2x 4. g(x) = 2|x| 2 5. g(x) = 2.2(x+ 2) 2 Algebra II 1

Algebra II 17

a. Write a function g whose graph is a horizontal shrink of the graph of f by a factor of 1/3

a. Write a function h whose graph is a vertical stretch of the graph of f by a factor of 2.

Page 18: 1. g(x) = -x + 2 2. g(x) = x 2 2 3. g(x)= 2 0.2x 4. g(x) = 2|x| 2 5. g(x) = 2.2(x+ 2) 2 Algebra II 1

Algebra II 18

a. Write a function g whose graph is a horizontal stretch of the graph of f by a factor of 5

a. Write a function h whose graph is a vertical shrink of the graph of f by a factor of 0.25.

Page 19: 1. g(x) = -x + 2 2. g(x) = x 2 2 3. g(x)= 2 0.2x 4. g(x) = 2|x| 2 5. g(x) = 2.2(x+ 2) 2 Algebra II 1

Algebra II 19

a. Write a function g whose graph is a horizontal shrink of the graph of f by a factor of 1/3

a. Write a function h whose graph is a vertical stretch of the graph of f by a factor of 2.

Page 20: 1. g(x) = -x + 2 2. g(x) = x 2 2 3. g(x)= 2 0.2x 4. g(x) = 2|x| 2 5. g(x) = 2.2(x+ 2) 2 Algebra II 1

Algebra II 20

Write the graph of g such that it is a vertical shrink by a factor of 0.25 followed by a translation 3 units up of the graph of f.

Page 21: 1. g(x) = -x + 2 2. g(x) = x 2 2 3. g(x)= 2 0.2x 4. g(x) = 2|x| 2 5. g(x) = 2.2(x+ 2) 2 Algebra II 1

Algebra II 21

Let the graph of g be a translation 6 units down followed by a reflection in the x-axis of the graph of f. Write a rule for g.

Page 22: 1. g(x) = -x + 2 2. g(x) = x 2 2 3. g(x)= 2 0.2x 4. g(x) = 2|x| 2 5. g(x) = 2.2(x+ 2) 2 Algebra II 1

Algebra II 22

1. f(x) = 3x; translation 5 units up2. f(x) = |x| – 3; translation 4 units to the

right.3. f(x) = –|x+2| – 1 reflection in the x-axis4. f(x) = ½x + 1; reflection in the y-axis 5. f(x) = 4x + 2; horizontal stretch by a

factor of 26. f(x) = |x | – 3; vertical shrink by a factor

of 1/3

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