Question

How does the graph of g(x) = (x − 8)3 + 3 compare to the parent function f(x) = x3?

a. g(x) is shifted 8 units to the left and 3 units up.
b. g(x) is shifted 3 units to the right and 8 units down.
c. g(x) is shifted 8 units to the right and 3 units up.
d. g(x) is shifted 3 units to the right and 8 units up.

Answer 1

The right answer is C.

Explanation:

The parent function is:

`f(x)=x^3`

If something is subtracted from variable
`x` it means the graph shifted toward right and something is added to
`y` value then the graph is shifted up.

`f(x)=(x-8)^3`

graph shifted toward right by
`8` units right

`f(x)=(x-8)^3+3`

graph shifted toward right by
`3` units up

Thus the new function is:

`g(x)=(x-8)^3+3`