Problem 4 Stretching and Compressing a Function

The table below represents the function f(x). What are corresponding values of g(x) and possible graphs for the transformation g ( x ) = 3 f ( x ) ? g open x close equals 3 f open x close question mark

• Step 1 Multiply each value of f(x) by 3 to find each corresponding value of g(x).

  x	f(x)	3f(x)	g(x)
  − 5 negative 5	2	3(2)	6
  − 2 negative 2	2	3(2)	6
  0	− 3 negative 3	3 ( − 3 ) 3 open negative 3 close	− 9 negative 9
  3	1	3(1)	3
  5	− 2 negative 2	3 ( − 2 ) 3 open negative 2 close	− 6 negative 6

  Think

  Is this a vertical stretch or compression?

  3 is greater than 1, so this is a vertical stretch.

• Step 2 Use the values from the table in Step 1. Draw simple graphs for f(x) and g(x).

  x	f(x)
  − 5 negative 5	2
  − 2 negative 2	2
  0	− 3 negative 3
  3	1
  5	− 2 negative 2

  
  Image Long Description

✓ Got It?

4. 1. For the function f(x) shown in Problem 4, what are the corresponding table and graph for the transformation h ( x ) = 1 3 h open x close equals , 1 third f(x)?
   2. Reasoning If several transformations are applied to a graph, will changing the order of transformations change the resulting graph? Explain.

Take Note Concept Summary: Transformations of f(x)