Question

The graph of f(x) is obtained by reflecting the graph of g(x)=3|x| over the x-axis.

Answer 1

Answer:

Choice B), $f(x) = -3|x|$.

Step-by-step explanation:

Each point on the graph of $g(x)$ can be represented as $(x, g(x))$.

When the graph of $g(x)$ 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, $1$ (same as $+1$) will become $-1$, and vice versa. In general, $(x, g(x))$ will become $(x, -g(x))$.

On the other hand, points on the graph of $f(x)$ can be represented as $(x, f(x))$. $f(x)$ is the reflection of $g(x)$, so $(x, -g(x))$ and $(x, f(x))$ shall be equivalent. In other words,

$f(x) = -g(x) = - 3|x|$.