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)
f  x   x3
f  x   x4
Translating a Polynomial Function
3
f
x

x


• For
, write the rule for each function and sketch its
graph, sketch the parent graph.
g  x  x  2
3
h(x) = (x + 3)3 – 6
Reflecting a Polynomial Function
• For f(x) = x3, write the rule for each function and sketch its
graph and parent graph
g  x    x3
g  x  x
3
Compressing and Stretching Polynomial
Functions
4
• Let f(x) = x . Graph f and g on the same coordinate
plane. Describe g as a transformation of f.
1 4
g  x  x
2
1 
g  x   x 
4 
4
Combining Transformations
• Write a function rule that transforms f(x) = x3 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) = x4 in each of the following ways.
Compress horizontally by a factor of ½, shift the 5 units left, and shift 2
units up .