6.2 Review Worksheet, Part 2
6.2.4 Transforming Polynomial Functions For f ( x ) = x 3 − 4, write the rule for each function and sketch its graph. 1. g ( x ) = f ( x ) − 3 2. h ( x ) = f ( x − 3)
3. j ( x ) = f ( x ) + 5
Let f ( x ) = x 3 − 2 x 2 + 5 x − 3. Write a function g that performs each transformation. 4. Reflect f ( x ) across the x -axis. 5. Reflect f ( x ) across the y -axis.
Let f ( x ) = 2 x 4 − 8 x 2 − 2. Graph f and g on the same coordinate plane. Describe g as a transformation of f . 6. g ( x ) = 2 f ( x ) 7. = g x f x ( ) ( ) 8. = g x f x ( )
1 2
1 2
Write a function that transforms f ( x ) = x 4 − 6 in each of the following ways. Support your solution by using a graphing calculator. 9. Reflect across the x -axis, and move the x -intercept 3 units left.
10. Compress vertically by a factor of 1 3
,, and move 1 unit up.
11. Stretch horizontally by a factor of 2, move 4 units right, and reflect across the y -axis.
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