Horizontal Line Test

If you are given a graph, how do you know if an inverse of a function is also a function?

You will use the horizontal line test. The horizontal line test states that the inverse of a function is a function if and only if every horizontal line intersects the graph of the given function at no more than one point.

Let’s take a look at an example. Is the inverse of the following graph also a function?

Is the inverse of this graph a function?

If we use the vertical line test we can see that this graph represents a function but what about its inverse? Is that also a function? That is when the horizontal line test comes in handy.

Analyze the following graph. Click the Play button to see the horizontal line test performed:

Notice that the horizontal line crosses the graph at two points. This means that the horizontal line test fails, and the inverse of the graph is not a function. Click the Play button below to see the horizontal line test performed again.

When we draw a horizontal line through this graph, the horizontal line hits the graph in one point. This means that according to the horizontal line test, the inverse of the graph is a function.