Question

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

Explanation:

Step1: Analyze the functions

We have \( f(x)= -8x - 8\) and \( g(x)=-4x - 4\). Notice that \( g(x)=\frac{1}{2}(-8x - 8)=\frac{1}{2}f(x)\).

Step2: Recall transformation rules

For a function \( y = a\cdot f(x)\), if \( 0 < |a| < 1\), it is a vertical shrink. Here \( a=\frac{1}{2}\), which satisfies \( 0<\frac{1}{2}< 1\). So the transformation from \( f(x)\) to \( g(x)\) is a vertical shrink.

Answer:

vertical shrink