Question

what kind of transformation converts the graph of f(x) = -4|x| + 4 into the graph of g(x) = -8|x| + 4? vertical stretch vertical shrink horizontal shrink horizontal stretch

Explanation:

Step1: Identify function transformation form

For functions $f(x)$ and $g(x) = a \cdot f(x) + k$, $a$ affects vertical scaling. Here, $f(x) = -4|x| + 4$, $g(x) = -8|x| + 4 = 2(-4|x|) + 4 = 2f(x) - 4$ (the constant term shift does not affect scaling).

Step2: Analyze scaling factor

The vertical scaling factor $a=2$, where $|a|>1$ indicates a vertical stretch.

Answer:

vertical stretch