Question

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


Which represents g(x), the translated function?

g(x) = (x – 5)3 + 3
g(x) = (x + 3)3 – 5
g(x) = (x – 3)3 + 5
g(x) = (x + 5)3 – 3

Answer 1

I can’t see the graph you mention. Can you either upload the image or tell me the coordinates of a key point on g(x) (for a cubic the easiest is the inflection point / “center” of the S-shape)?

Tip to identify it yourself:
- The parent f(x)=x^3 has its inflection (center) at (0,0).
- A translation that moves that point to (h,k) gives g(x) = (x − h)^3 + k.
So read off the new center (h,k) on the graph and pick the option with (x − h)^3 + k.

(For reference, the four answer choices correspond to these shifts:
- (x − 5)^3 + 3 → center at (5, 3)
- (x + 3)^3 − 5 → center at (−3, −5)
- (x − 3)^3 + 5 → center at (3, 5)
- (x + 5)^3 − 3 → center at (−5, −3) )

If you upload the graph or tell me the new center, I’ll pick the correct choice.