Question

guided solution
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complete the following.
part a. describe the transformation of $f$ represented by $g$.
$f(x)=\log_{4}x$, $g(x)=3 \log_{4} x-5$
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

Explanation:

Step1: Identify vertical stretch factor

For $g(x)=3\log_4 x -5$, the coefficient of $f(x)=\log_4 x$ is 3, so this is a vertical stretch.

Step2: Identify vertical translation direction

The term $-5$ outside the log function shifts the graph downward.

Step3: Identify translation magnitude

The constant term is 5, so the translation is 5 units.

Answer:

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