Transformations of Graphs Date Period - Kuta Software

Kuta Software - Infinite Precalculus

Name___________________________________

Transformations of Graphs

Date________________ Period____

Describe the transformations necessary to transform the graph of f (x) (solid line) into that of g(x) (dashed line).

1) y

2) y

x

x

Describe the transformations necessary to transform the graph of f (x) into that of g(x).

3) f (x) x g(x) x

4) f (x)x g(x)(x)

Transform the given function f (x) as described and write the resulting function as an equation.

5) f (x)x

expand vertically by a factor of translate down units

6) f (x)

x compress horizontally by a factor of translate left units

7) f (x) x

expand horizontally by a factor of translate right unit translate up units

8) f (x) x

compress vertically by a factor of reflect across the x-axis translate right units translate down units

-1-

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Write g(x) (dashed line) in terms of f (x) (solid line).

9) y

10) y

x

x

11) y

x

12) y

x

Identify the parent function f (x) and write an equation for the function given.

13) y

14) y

x

x

-2-

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Worksheet by Kuta Software LLC

Kuta Software - Infinite Precalculus

Name___________________________________

Transformations of Graphs

Date________________ Period____

Describe the transformations necessary to transform the graph of f (x) (solid line) into that of g(x) (dashed line).

1) y

2) y

x

x

reflect across the x-axis translate left units

compress vertically by a factor of translate up units

Describe the transformations necessary to transform the graph of f (x) into that of g(x).

3) f (x) x g(x) x

4) f (x)x g(x)(x)

expand vertically by a factor of reflect across the x-axis translate down unit

expand vertically by a factor of translate left unit

Transform the given function f (x) as described and write the resulting function as an equation.

5) f (x)x

expand vertically by a factor of translate down units

g(x)x

6) f (x)

x compress horizontally by a factor of translate left units

g(x)

(x)

7) f (x) x

expand horizontally by a factor of translate right unit translate up units

g(x) (x)

8) f (x) x

compress vertically by a factor of reflect across the x-axis translate right units translate down units

g(x) x

-1-

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Worksheet by Kuta Software LLC

Write g(x) (dashed line) in terms of f (x) (solid line).

9) y

10) y

x

x

g(x) f ((x))

( ) g(x) f

x

11) y

x

g(x) f (x)

12) y

x

g(x) f (x)

Identify the parent function f (x) and write an equation for the function given.

13) y

14) y

x

Parent: f (x) x g(x) (x)

x

Parent: f (x)x g(x)x

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-2-

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