Question

On a coordinate plane, 2 cube root functions are shown. The first cube root function is a solid line and goes through (negative 8, 2), has an inflection point at (3.5, 4), and goes through (4, 5). The second cube root function is a dashed line and is represented by the equation f (x) = RootIndex 3 StartRoot x EndRoot. The function goes through (negative 8, negative 2), has an inflection point at (0, 0), and goes thorugh (8, 2).
Which equation is graphed along with the parent function?

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

Answer 1

g(x) = ∛(x − 3) + 4

Reason: The cube root's inflection (0,0) is shifted right 3 and up 4 to (3,4), so the transform is ∛(x−3)+4. It also fits (4,5): ∛(4−3)+4 = 1+4 = 5.