Question

Given `-f(x)`, how do you describe the transformation?

Answer 1

A reflection about the `x`-axis.

Explanation:

For any function `f`, its output at any given input `x` is just `f(x)`.

When we take that output `f(x)` and make it negative (i.e. `-f(x)`), we're just flipping the sign of the output—positives become negatives, and vice versa.

Let's say that when `x=3,` we have `f(x)=5`.
Thus, when `x=3,` we have `"-"f(x)="-"5`.

All that happens is the sign of the output value changes—points that were once above the `x`-axis are now below, with no shift left or right.

This is simply stated as a reflection where the mirror is the `x`-axis, also called a reflection about the `x`-axis.