Question

Your friend hands you a graph of the performance statistics of the newest car to roll off the assembly line. He says, "I know this graph is f(x) = -4(x - 5)3 + 7 but I can't remember how it is related to the graph of x3." Explain to your friend how the graph f(x) is a translation of the graph x3.

Answer 1

\(\large f(x)=x^3\)

If you have this form of the equation:
\(\large f(x) = a(x-h)^3+k\)

a = stretch or compression. If negative, it indicates a reflection as well
h = horizontal translation (right or left)
k = vertical translation (up down)

Answer 2

Some useful information:
h>0 means translation to the right
k>0 means translation upwards.
|a|>1 means vertical stretch
0<|a|<1 means vertical compression
as @StudyGurl14 mentioned, a<0 means reflection about the x-axis.