The Horizontal Line Test is a great way to check if a function has an inverse.

Here’s how it works:

If you draw a horizontal line on the graph of a function, you want to see how many times it crosses the graph.

• If the line crosses the graph more than once, that means the function doesn't have an inverse.
• If it crosses only once, then the function does have an inverse.

Why is this important? Well, a function should give one output for every input. If a horizontal line meets the graph at multiple places, it means there are different outputs for the same input, which breaks the rules of a function.

Here’s a simple way to do the Horizontal Line Test:

1. Graph the Function: First, draw the function on a coordinate plane.

2. Draw Horizontal Lines: You can imagine or actually draw horizontal lines across the graph at different heights (these are your $y$ values).

3. Count Intersections: See how many times each horizontal line crosses the graph.

   • If it crosses more than once: The function does NOT have an inverse.
   • If it crosses just once: Yay! The function has an inverse.

This test works really well with different kinds of functions. For example, with quadratic functions like $y = x^2$, you can see that horizontal lines hit the graph two times, which means no inverse.

On the other hand, for linear functions like $y = 2x + 3$, a horizontal line only crosses once, so these functions do have inverses.

Just remember, it’s all about making sure that each input has one unique output!