Question

1. write a rule for $g$ that represents the indicated transformations of the graph of $f$.

$f(x) = \log_{6} x$; vertical stretch by a factor of 6, followed by a translation 5 units down
$g(x) = \square$

Explanation:

Step1: Apply vertical stretch by 6

Multiply $f(x)$ by 6:
$6f(x) = 6\log_{6} x$

Step2: Apply translation 5 units down

Subtract 5 from the stretched function:
$g(x) = 6\log_{6} x - 5$

Answer:

$g(x) = 6\log_{6} x - 5$