Question

$f(x) = log_4 x$, $g(x) = 3 log_4 x - 5$
the graph of $g$ is a $\boldsymbol{square}$ by a factor of $\boldsymbol{square}$ , followed by a translation $\boldsymbol{square}$ units $\boldsymbol{square}$ of the graph of $f$.
options:
2, 3, 5, 6
up, down, left, right
vertical shrink, vertical stretch, horizontal shrink, horizontal stretch

Explanation:

Step1: Identify vertical transformation

For $g(x) = 3\log_4 x - 5$, the coefficient 3 on $\log_4 x$ means a vertical stretch by factor 3, since $a\cdot f(x)$ with $a>1$ is vertical stretch by $a$.

Step2: Identify vertical translation

The $-5$ at the end of $g(x) = 3\log_4 x - 5$ corresponds to $f(x)-k$, which is a translation down $k$ units, here $k=5$.

Answer:

The graph of $g$ is a vertical stretch by a factor of $\boldsymbol{3}$, followed by a translation $\boldsymbol{down}$ $\boldsymbol{5}$ units of the graph of $f$.