6.2.4 Transforming Polynomial Functions - Worksheet
Example 1: For f ( x ) = x 4 − 8, write the rule for each function, and sketch its graph. 1. g ( x ) = f ( x ) + 4 2. h ( x ) = f ( x − 2) 3. j ( x ) = f (3 x )
1 2
4. k ( x ) = f ( x ) = − k x f x ( ) ( )
Example 2: Let f ( x ) = − x 3 + 3 x 2 − 2 x + 1. Write a function g that performs each transformation. 5. Reflect f ( x ) across the y -axis. 6. Reflect f ( x ) across the x -axis.
Example 3: Let f ( x ) = x 3 − 4 x 2 + 2. Graph f and g on the same coordinate plane. Describe g as a transformation of f . 7. = g x f x ( ) 8. g ( x ) = 3 f ( x ) 9. g ( x ) = f (2 x ) + 4
1 2
Example 4: Write a function that transforms f ( x ) = 4 x 3 + 2 in each of the following ways. Support your
solution by using a graphing calculator. 10. Compress vertically by a factor of 1 2
,, and move the y -intercept 2 units down.
11. Reflect across the y -axis, and compress horizontally by a factor of 1 2 ..
12. Move 2 units right, move 3 units down, and reflect across the x -axis.
77
Made with FlippingBook - Share PDF online