Question

The parent function f(x) = x3 is translated to form g(x), as shown on the graph. The translated function can be written in the form
g(x) = (x – h)3 + k.


What are the values of h and k?


h = 4
k = –2

h = –4
k = –2

h = 4
k = 2

h = –4
k = 2

Answer 1

I can’t see the graph you mention. To pick the right option, locate the inflection point (the “center” of the cubic where it switches concavity). For f(x)=x^3 that point is at (0,0); after the translation it will be at (h,k). So read off the coordinates of that inflection point on the graph — those coordinates are h and k.

Quick checks:
- If the inflection point is at (4, −2) then choose h = 4, k = −2.
- If it’s at (−4, −2) choose h = −4, k = −2.
- If it’s at (4, 2) choose h = 4, k = 2.
- If it’s at (−4, 2) choose h = −4, k = 2.

(Another check: the point that was (1,1) on x^3 moves to (h+1, k+1) on g(x); similarly (−1,−1) moves to (h−1, k−1).)

Upload the graph or tell me the coordinates of a clear point (especially the inflection point) and I’ll pick the correct option.