Question

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

Which equation describes f(x)?

A) f(x)=3|x|
B) f(x)= -3|x|
C) f(x)= |x+3|
D) f(x)= - |x+3)

Answer 1

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

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|`.