Answer:
Choice B), [tex]f(x) = -3|x|[/tex].
Step-by-step explanation:
Each point on the graph of [tex]g(x)[/tex] can be represented as [tex](x, g(x))[/tex].
When the graph of [tex]g(x)[/tex] is reflected over the x-axis, each point on the graph is also reflected over the x-axis. The x-coordinate of each point will not change but the sign in front of the y-coordinate will flip. For example, [tex]1[/tex] (same as [tex]+1[/tex]) will become [tex]-1[/tex], and vice versa. In general, [tex](x, g(x))[/tex] will become [tex](x, -g(x))[/tex].
On the other hand, points on the graph of [tex]f(x)[/tex] can be represented as [tex](x, f(x))[/tex]. [tex]f(x)[/tex] is the reflection of [tex]g(x)[/tex], so [tex](x, -g(x))[/tex] and [tex](x, f(x))[/tex] shall be equivalent. In other words,
[tex]f(x) = -g(x) = - 3|x|[/tex].
