1. Objective
Transform polynomial functions.

2. You can perform the same transformations on polynomial functions that you performed on quadratic and linear functions.

3. Check It Out! Example 1a
For f(x) = x3 + 4, write the rule for each function and sketch its graph.

4. Check It Out! Example 1b
For f(x) = x3 + 4, write the rule for each function and sketch its graph.

5. Reflect f(x) across the x-axis.
Check It Out! Example 2a
Let f(x) = x3 – 2x2 – x + 2. Write a function g that performs each transformation.
Reflect f(x) across the x-axis.

6. Reflect f(x) across the y-axis.
Check It Out! Example 2b
Let f(x) = x3 – 2x2 – x + 2. Write a function g that performs each transformation.
Reflect f(x) across the y-axis.

7. Check It Out! Example 3a
Let f(x) = 16x4 – 24x Graph f and g on the same coordinate plane. Describe g as a transformation of f. 1 4
g(x) = f(x)

8. g(x) is a horizontal stretch of f(x).
Check It Out! Example 3b
Let f(x) = 16x4 – 24x Graph f and g on the same coordinate plane. Describe g as a transformation of f. 1 2
g(x) = f( x)
g(x) = 16( x)4 – 24( x)2 + 4 1 2
g(x) = x4 – 3x2 + 4
g(x) is a horizontal stretch of f(x).

9. Check It Out! Example 4a
Write a function that transforms f(x) = 8x3 – 2 in each of the following ways. Support your solution by using a graphing calculator.
Compress vertically by a factor of , and move the x-intercept 3 units right. 1 2

10. Check It Out! Example 4b
Write a function that transforms f(x) = 6x3 – 3 in each of the following ways. Support your solution by using a graphing calculator.
Reflect across the x-axis and move the x-intercept 4 units left.