QuestionExplain how to determine if a function has a vertical stretch or vertical compression as a result of the constant $a$ given that $g(x)=a f(x)$.

Studdy Solution
If $a$ is negative, the function $g(x) = a f(x)$ not only stretches or compresses but also reflects the graph of $f(x)$ across the x-axis. The conditions for stretch or compression remain the same, but the reflection is an additional transformation.
In summary, $a$ causes a vertical stretch if $|a| > 1$, a vertical compression if $0 < |a| < 1$, and reflects the graph if $a$ is negative. If $a = 0$, the graph is a constant line on the x-axis.