Problem
BB.5 Transformations of absolute value functions: translations and reflections 9TC Find $g(x)$, where $g(x)$ is the reflection across the $y$-axis of $f(x)=|x|$. Write your answer in the form $a|x-h|+k$, where $a, h$, and $k$ are integers. \[ g(x)= \] Submit
Solution
Step 1 ：The function $f(x)=|x|$ is already symmetric with respect to the y-axis. Therefore, reflecting it across the y-axis will not change the function. So, $g(x) = f(x) = |x|$.
Step 2 ：This can be written in the form $a|x-h|+k$ as $1|x-0|+0$.
Step 3 ：Final Answer: $g(x) = \boxed{1|x-0|+0}$
