Question

part a. describe the transformation of $f$ represented by $g$.
$f(x)=\log_{1/3}x$, $g(x)=\log_{1/3}(-x)+6$
the graph of $g$ is a $\boldsymbol{\square^1}$ in the $\boldsymbol{\square^2}$, followed by a translation $\boldsymbol{\square^3}$ units $\boldsymbol{\square^4}$ of the graph of $f$.

options:
3, 4, 6, 8
up, down, left, right
vertical shrink, vertical stretch, horizontal shrink
reflection, translation, x-axis

Explanation:

Step1: Identify reflection 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 vertical translation

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

Answer:

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