Question

Which describes the transformations from the graph of f(x) to the graph of - f(x - 4)
?

Answer 1

Explanation:

f(x) = (x+2)² - 2

-f(x-4) means multiply the whole function by -1 and substitute x for x-4

-f(x-4) = -[((x-4)+2)² - 2] simplify the -4 and 2

= -[(x-2)² -2] distribute the -

= -(x-2)² + 2

1. the new function is now facing down, reflected across the x-axis

2. the new vertex is (2, 2) the old one was (-2, -2)

-shifted 4 units right

- shifted 4 units up