Hello!
Given the function, f(x) = 5x, find the equation where the function f, is reflected over the x-axis.
There are two types of reflections. One reflection is over the x-axis (the most common) and over the y-axis.
Say for example, we are given the point (x, y), and we want to reflect it over the x-axis. If the point (x, y) is reflected over the x-axis, then the point is (x, -y). Why? It's because y-values above the x-axis are POSITIVE while x-values below are NEGATIVE.
So, an equation to show this is: y = -f(x).
To find it, we multiply the entire function, which is f(x), by a negative. Since f(x) = 5x, the transformed function is f(x) = -5x.
Therefore, the function rule for the function shown is -f(x).
