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# Transformation of Functions Exploration Lesson

Module by: Debbie Trahan. E-mail the author

Summary: In this module the students will explore transformations of a square root function algebraically, graphically, and using a table of values.

## Transformation of Functions Exploration

In this lesson you will be investigating the transformation of a function by examining the notations, the tables of values and the graphs of the function and its transformations. After working through problems 1 - 11, you will be able to explain the effects of the following transformations on the graph of the function fx f x if c>0 c 0 .

fx+c f x c ; fxc f x c ; fx+c f x c ; fxc f x c ; cfx c f x if 0<c<1 0 c 1 ; cfx c f x if c>1 c 1 ; fcx f c x if 0<c<1 0 c 1 ; fcx f c x if c>1 c 1 ; fx f x ; fx f x .

In problems 1 - 11, you will examine the function fx=x f x x and its transformations.

### Exercise 1

Given the function fx=x f x x and the table of values for fx f x , graph y=fx y f x on the grid (figure 1).

## Exercise 2

The function y=x+2 y x 2 is a transformation of fx f x . The notation fx+2 f x 2 can be used to show this transformation. Graph fx f x in red. Complete the table of values then use the table of values to help you graph the transformation (figure 3) . Explain how the transformation changed the graph of fx f x .

## Exercise 3

The function y=x1 y x 1 is a transformation of fx f x . The notation fx1 f x 1 can be used to show this transformation. Graph fx f x in red. Complete the table of values then use the table of values to help you graph the transformation (figure 5) . Explain how the transformation changed the graph of fx f x .

## Exercise 4

The function y=-3+x y -3 x is a transformation of fx f x . The notation fx3 f x 3 can be used to show this transformation. Graph fx f x in red. Complete the table of values then use the table of values to help you graph the transformation (figure 7) . Explain how the transformation changed the graph of fx f x .

## Exercise 5

The function y=1+x y 1 x is a transformation of fx f x . The notation fx+1 f x 1 can be used to show this transformation. Graph fx f x in red. Complete the table of values then use the table of values to help you graph the transformation (figure 9) . Explain how the transformation changed the graph of fx f x .

## Exercise 6

The function y=2x y 2 x is a transformation of fx f x . The notation 2fx 2 f x can be used to show this transformation. Graph fx f x in red. Complete the table of values then use the table of values to help you graph the transformation (figure 11) . Explain how the transformation changed the graph of fx f x .

## Exercise 7

The function y=.5x y .5 x is a transformation of fx f x . The notation .5fx .5 f x can be used to show this transformation. Graph fx f x in red. Complete the table of values then use the table of values to help you graph the transformation (figure 13) . Explain how the transformation changed the graph of fx f x .

## Exercise 8

The function y=2x y 2 x is a transformation of fx f x . The notation f2x f 2 x can be used to show this transformation. Graph fx f x in red. Complete the table of values then use the table of values to help you graph the transformation (figure 15) . Explain how the transformation changed the graph of fx f x .

## Exercise 9

The function y=.5x y .5 x is a transformation of fx f x . The notation f.5x f .5 x can be used to show this transformation. Graph fx f x in red. Complete the table of values then use the table of values to help you graph the transformation (figure 17) . Explain how the transformation changed the graph of fx f x .

## Exercise 10

The function y=x y x is a transformation of fx f x . The notation fx f x can be used to show this transformation. Graph fx f x in red. Complete the table of values then use the table of values to help you graph the transformation (figure 19) . Explain how the transformation changed the graph of fx f x .

## Exercise 11

The function y=x y x is a transformation of fx f x . The notation fx f x can be used to show this transformation. Graph fx f x in red. Complete the table of values then use the table of values to help you graph the transformation (figure 21) . Explain how the transformation changed the graph of fx f x .

Answer questions 12 - 21 to test your knowledge of functions and their transformations.

## Exercise 12

Given the function gx g x , c c is a real number , and c>0 c 0 explain how the transformation gx+c g x c changes the graph of gx g x .

## Exercise 13

Given the function gx g x , c c is a real number , and c>0 c 0 explain how the transformation gxc g x c changes the graph of gx g x .

## Exercise 14

Given the function gx g x , c c is a real number , and c>0 c 0 explain how the transformation gx+c g x c changes the graph of gx g x .

## Exercise 15

Given the function gx g x , c c is a real number , and c>0 c 0 explain how the transformation gxc g x c changes the graph of gx g x .

## Exercise 16

Given the function gx g x , c c is a real number , and c>1 c 1 explain how the transformation gcx g c x changes the graph of gx g x .

## Exercise 17

Given the function gx g x , c c is a real number , and 0<c<1 0 c 1 explain how the transformation gcx g c x changes the graph of gx g x .

## Exercise 18

Given the function gx g x , c c is a real number , and c>1 c 1 explain how the transformation cgx c g x changes the graph of gx g x .

## Exercise 19

Given the function gx g x , c c is a real number , and 0<c<1 0 c 1 explain how the transformation cgx c g x changes the graph of gx g x .

## Exercise 20

Given the function gx g x explain how the transformation gx g x changes the graph of gx g x .

## Exercise 21

Given the function gx g x explain how the transformation gx g x changes the graph of gx g x .

## Transformations of Functions Exploration Modules

After you have completed this lesson you can continue to explore transformations of functions by choosing a module listed below.

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