Question

The function f(x) = RootIndex 3 StartRoot x EndRoot is reflected over the x-axis to create the graph of g(x) = Negative RootIndex 3 StartRoot x EndRoot.

Which is the graph of g(x)?

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

Answer 1

Reflecting f(x)=∛x across the x-axis gives g(x)=−∛x, so every y-value is multiplied by −1. f(x) has points (−8, −2), (0,0), (8,2), so g(x) has (−8, 2), (0,0), (8, −2).

Thus the correct graph is: "On a coordinate plane, a cube root function goes through (negative 8, 2), has an inflection point at (0, 0), and goes through (8, negative 2)."