Question

The graph of the cube root parent function y = RootIndex 3 StartRoot x EndRoot is translated to form f(x) shown on the graph.

On a coordinate plane, a cube root function goes through (negative 7, 0), has an inflection point at (negative 6, 1), and goes through (2, 3).

Which equation represents f(x)?

f(x) = RootIndex 3 StartRoot x + 6 EndRoot + 1
f(x) = RootIndex 3 StartRoot x minus 6 EndRoot + 1
f(x) = RootIndex 3 StartRoot x + 6 EndRoot minus 1
f(x) = RootIndex 3 StartRoot x minus 6 EndRoot minus 1

Answer 1

f(x) = ∛(x + 6) + 1

Reason: the cube root's inflection point is at (h,k). Here (h,k)=(-6,1), so f(x)=∛(x-(-6))+1 = ∛(x+6)+1. Check: f(-7)=∛(-1)+1=0 and f(2)=∛8+1=3.