Question

$f(x) = \log_{1/3}x$, $g(x) = \log_{1/3} (-x)+6$
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:
3, 4, 6, 8
up, down, left, right
vertical shrink, vertical stretch, horizontal shrink, horizontal stretch
reflection, translation
x-axis, y-axis

Explanation:

Step1: Identify first transformation

For $f(x)=\log_{1/3}x$, replacing $x$ with $-x$ gives $\log_{1/3}(-x)$, which is a reflection in the $y$-axis.

Step2: Identify second transformation

Adding $6$ to $\log_{1/3}(-x)$ gives $g(x)=\log_{1/3}(-x)+6$, which is a translation 6 units up.

Answer:

The graph of $g$ is a reflection in the $y$-axis, followed by a translation 6 units up of the graph of $f$.