Question

The graph of g(x) is a translation of y = RootIndex 3 StartRoot x EndRoot.

On a coordinate plane, a cube root function goes through (negative 6, negative 2), has an inflection point at (4, 0), and goes through (10, 2).

Which equation represents g(x)?

g(x) = RootIndex 3 StartRoot x minus 4 EndRoot
g(x) = RootIndex 3 StartRoot x + 4 EndRoot
g(x) = RootIndex 3 StartRoot x EndRoot + 1.5
g(x) = RootIndex 3 StartRoot x EndRoot minus 1.5

Answer 1

y = ∛x has its inflection point at (0,0). Shifting it right 4 units moves the inflection to (4,0), so the translation is x → x − 4.

Thus g(x) = ∛(x − 4).