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

Let's just say you have some general functions f(x) and g(x), and you know that:
\[g(x) = a*f(x-h) + k\]
a, h, and k all do different things to f(x).

a will stretch or squish f(x) vertically. If a=2, g(x) will be twice as tall as f(x). If a is negative, g(x) will be f(x) flipped and stretched.

h is how far to the RIGHT a function is shifted. This is kind of tricky, since it has a negative sign in front of it.

k is how far UP the function is shifted. This makes more sense, since the sign in front of it is positive.