Chapter 2 - Functions, Equations, and Graphs - 2-6 Families of Functions - Practice and Problem-Solving Exercises - Page 104: 24

$g(x)=-3x$

Recall: (1) The graph of $y=f(-x)$ involves a reflection about the $y$-axis of the parent function $f(x)$. (2) The graph of $y=-f(x)$ involves a reflection about the $x$-axis of the parent function $f(x)$. Thus, when $f(x)=3x$ is reflected about the $y$-axis, the equation of the new function $g(x)$, is: \begin{align*} g(x)&=f(-x)\\ g(x)&=3(-x)\\ g(x)&=-3x \end{align*}