Question

$f(x) = \log_{1/5} x$, $g(x) = -\log_{1/5} (x-7)$
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
vertical shrink, vertical stretch, horizontal shrink, horizontal stretch
reflection, translation, x-axis, y-axis

Explanation:

Step1: Identify reflection transformation

The function $g(x)$ has a negative sign in front of the logarithm, compared to $f(x)=\log_{1/5}x$. This corresponds to a reflection in the $x$-axis.

Step2: Identify translation transformation

Inside the logarithm, we have $(x-7)$ instead of $x$. For a function $f(x-h)$, this represents a translation $h$ units to the right. Here, $h=7$, so it is 7 units right.

Answer:

1. reflection
2. x-axis
3. 7
4. right

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