Write an equation for the function whose graph is described.

Question

The shape of f(x)= x³, but shifted four units to the left, nine units down, and then reflected in the y-axis (in that order.)

Answer 1

Start with the function f(x)= x³. Then

1. Shift 4 units to the left (replace x by x+4): f(x) = (x+4)³.

2. Shift 9 units down (replace f(x) by f(x)+9): f(x) + 9 = (x+4)³.

3. Reflect in the y-axis (replace x by -x): f(x) + 9 = (-x+4)³.

Simplifying, we get f(x) = (4-x)³ - 9.