Question

Which graph represents y = RootIndex 3 StartRoot x + 6 EndRoot minus 3?
On a coordinate plane, a cubic function is shown. It has a point of inflection at x = negative 3 and it crosses the x-axis at x = negative 1.
On a coordinate plane, a cubic function is shown. It has a point of inflection at x = negative 3 and it crosses the x-axis at x = negative 5.
On a coordinate plane, a cubic function is shown. It has a point of inflection at x = 6 and it crosses the x-axis at x = 7.
On a coordinate plane, a cubic function is shown. It has a point of inflection at x = 6 and it crosses the x-axis at x = 5.

Answer 1

y = ∛(x + 6) − 3 is a cube‑root graph shifted left 6 and down 3, so its point of inflection is at (−6, −3).

The x‑intercept is found by setting y = 0:
0 = ∛(x + 6) − 3 → ∛(x + 6) = 3 → x + 6 = 27 → x = 21.

None of the four described graphs match (their inflection x‑coordinates are −3 or 6, and their x‑intercepts are −1, −5, 7, or 5), so none of the options is correct.