Question

The graph shows the function f(x).

On a coordinate plane, a cube root function goes through (8, 2), has an inflection point at (0, negative 1), and goes through (8, negative 3).

Which equation represents f(x)?

f(x) = Negative RootIndex 3 StartRoot x minus 1 EndRoot
f(x) = Negative RootIndex 3 StartRoot negative x EndRoot minus 1

Answer 1

The cube-root parent has equation a∛(x − h) + k with inflection at (h, k). Since the inflection is at (0, −1), h = 0 and k = −1, so f(x) = a∛x − 1. Of the two choices, -∛(-x) − 1 = ∛x − 1 matches that form. (The other choice, −∛(x − 1), has inflection at (1, 0), so it is incorrect.)