SECTION 3-8 TRANSFORMING POLYNOMIAL FUNCTIONS

Objectives: Transform Polynomial Functions

Transforming Polynomial Functions • You can perform the same transformations on polynomial functions that you performed on quadratic and linear functions

Transforming Polynomial Functions • Graph the parent functions ( YOU NEED TO KNOW THESE) 

x

3 

x

4

• Translating a Polynomial Function   

x

3 graph, sketch the parent graph.

h(x) = (x + 3) 3 – 6

x

2

Reflecting a Polynomial Function • For

f

(

x

) =

x

3 , write the rule for each function and sketch its graph and parent graph    

x

3     3

Compressing and Stretching Polynomial • Let

f

(

x

) =

x

4 . Graph

f

Functions and

g

on the same coordinate plane. Describe

g

as a transformation of

f

. 4  1 2

x

4

x

Combining Transformations • Write a function rule that transforms

f

(

x

) =

x

3 in each of the following ways. Compress vertically by a factor of 1/3, and shift 2 units right. • Write a function that transforms

f

(

x

) =

x

4 in each of the following ways. Compress horizontally by a factor of ½, shift the 5 units left, and shift 2 units up .