Objective Transform polynomial functions.

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

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

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

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.

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.

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

g(x) is a horizontal stretch of f(x). Check It Out! Example 3b Let f(x) = 16x4 – 24x2 + 4. 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).

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

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.