Question

The graph of the parent function f(x) = x3 is translated to form the graph of g(x) = (x + 3)3 – 4. The point (0, 0) on the graph of f(x) corresponds to which point on the graph of g(x)?

Answer 1

f(x) + n - shift a graph of f n units up

f(x) - n - shift a graph of f n units down

f(x + n) - shift a graph of f n units left

f(x - n) - shift a graph of f n units right.

f(x) = x³, g(x) = (x + 3)³ - 4 = f(x + 3) - 4

3 units left and 4 units down.

(x, y) → (x - 3, y - 4)

therefore

(0, 0) → (0 - 3, 0 - 4) = (-3, -4).

Answer: (-3, -4).