Question

The graph of the parent function f(x) = x3 is translated such that the resulting graph can be represented by the function g(x) = (x – 1)3 + 1. Which is the graph of g(x)?

Answer 1

g(x) = (x − 1)^3 + 1 is the parent cubic f(x)=x^3 shifted right 1 unit and up 1 unit. Its inflection point (the "center" of the S-shape) is at (1,1). Key points: g(0)=0, g(1)=1, g(2)=2. So pick the cubic graph with that S-shape whose center is at (1,1) (equivalently passing through (0,0),(1,1),(2,2)).