## What is the horizontal line test?

In January of this year, we have discussed about the vertical line test. We have learned that if a vertical line intersect a graph more than once, then that graph is not a function. In this post, we learn about the horizontal line test and its relation to inverse functions.

Suppose we have a function $f$. Then, we input $x$ and call the output $f(x)$. If we do things backward, suppose we have the number $y$ which is in the range of $f$. What value should we input to $f$ to get $y$? Let’s have a more specific example.

Suppose we have the function $f(x) = x^2$. And we choose the number $y = 9$ which is in the range of $f$. What number should we input in $f$ to get $9$? Well, we will have two numbers, those are $3$ and $-3$. » Read more