Question

1. complete the following.

part a. describe the transformation of $f$ represented by $g$.
$f(x)=\log_{1/5} x$, $g(x)=-\log_{1/5} (x-7)$
the graph of $g$ is a $\boldsymbol{\square}$ in the $\boldsymbol{\square}$, followed by a translation
$\boldsymbol{\square}$ units $\boldsymbol{\square}$ of the graph of $f$.

options:
2, 3, 5, 6, 7
up, down, left, right

Explanation:

Step1: Identify reflection transformation

For $g(x) = -\log_{1/5}(x-7)$, the negative sign outside the parent function $f(x)=\log_{1/5}x$ represents a reflection over the x-axis.

Step2: Identify translation transformation

The $(x-7)$ inside the logarithm function means a horizontal translation. For $f(x-h)$, the graph shifts right by $h$ units. Here $h=7$, so it is a shift right 7 units.

Answer:

The graph of $g$ is a reflection over the x-axis in the x-axis, followed by a translation 7 units right of the graph of $f$.