Question

The graph of the parent function f(x) = x3 is translated to form g(x) = (x – 2)3 – 3. Which is the graph of g(x), the translated function?

Answer 1

g(x) = (x − 2)^3 − 3 is the graph of f(x)=x^3 shifted right 2 units and down 3 units.

Key features:
- Inflection point (the "center" of the cubic) at (2, −3).
- Example points: (2, −3), (3, −2), (1, −4).
- Same shape/orientation as x^3 (increasing, symmetric about the inflection point).
- Domain = (−∞, ∞), Range = (−∞, ∞).

So the correct graph is the standard cubic moved 2 to the right and 3 down.