Question

The parent function f(x) = x3 and a translation, g(x), are shown on the graph.


Which represents g(x), the translated function?

g(x) = (x + 4)3 + 6
g(x) = (x – 4)3 + 6
g(x) = (x + 6)3 – 4
g(x) = (x – 6)3 – 4

Answer 1

g(x) = (x − 4)^3 + 6

Reason: the cube function's inflection point at (0,0) moves to the graph's inflection point at (4,6), so the curve is shifted right 4 and up 6, i.e. replace x by (x−4) and add 6.