6.2.4 Transforming Polynomial Functions - Practice
1. For = − f x x ( ) 1 4 6, 3 , write the rule for g ( x ) = f ( x + 3) + 10 and sketch its graph.
2. Let f ( x ) = − x 3 − 8 x 2 − 9 x + 11. Write the function g that reflects f across the y -axis.
3. Let f ( x ) = 6 x 3 + 3 x 2 − 6 x + 9 and = g x f x ( ) ( ). Which of the following describes g as a function of f and gives the correct rule? ○ vertical compression g ( x ) = 2 x 3 + x 2 − 2 x + 3 ○ vertical stretch = + − + g x x x x ( ) 1 3 2 3 3 2
4. Let f ( x ) = x 3 − 5 x 2 + 2 x − 7 and g ( x ) = f (4 x ). Which of the following describes g as a function of f and gives the correct rule? ○ horizontal stretch; g ( x ) = 4 x 3 − 20 x 2 + 8 x − 28 ○ horizontal compression; g ( x ) = 64 x 3 − 80 x 2 + 8 x − 7 ○ vertical stretch; g ( x ) = 4 x 3 − 20 x 2 + 8 x − 28 ○ vertical compression; g ( x ) = 64 x 3 − 80 x 2 + 8 x − 7
2 9
1 3 1 3
○ horizontal stretch
= + − + g x x x x ( ) 2 9 2 9 3 2
○ horizontal compression g ( x ) = 2 x 3 + x 2 − 2 x + 3
5. Write the function that reflects f ( x ) = 7 x 3 + 4 x 2 − 11 across the x -axis and shifts it 3 units down.
6. The number of toys sold per month can be modeled by f ( x ) = 3 x 4 + 2 x 3 + 5 x + 10, where x represents the number of months since June. Let g ( x ) = f ( x ) + 3. Write the rule for g and explain the meaning of the transformation in terms of monthly toy sales.
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