Question

The graph of h(x) is a translation of f (x) = RootIndex 3 StartRoot x EndRoot.

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

Which equation represents h(x)?

h (x) = RootIndex 3 StartRoot x minus 2 EndRoot
h (x) = RootIndex 3 StartRoot x + 2 EndRoot
h (x) = RootIndex 3 StartRoot x EndRoot minus 2
h (x) = RootIndex 3 StartRoot x EndRoot + 2

Answer 1

h(x) = ∛(x + 2)

Reason: The parent ∛x has inflection at (0,0). To move the inflection to (-2,0) shift left 2, giving h(x)=∛(x+2). This also yields h(-3)=∛(-1)=-1 and h(-1)=∛1=1, matching the given points.