Question

If you vertically compress the absolute value parent function, f(x) = |x|, by a factor of 4, what is the equation of the new function?

Answer 1

Vertical stretch/compression is achieved by multiplying the function by a certain constant:

$f(x) \to k\cdot f(x)$

In particular, if $k>1$ the function is vertically stretched by a factor k, otherwise, if $0 < k < 1$, the function is vertically compressed by a factor k.

So, in your case, you want to multiply the function by 1/4:

$|x| \to \dfrac{1}{4}|x|$