Graphs are amazing tools that help us understand inverse functions, and they make learning fun! Let’s dive into how they work!

1. Visual Representation:

   • Graphs help us see the difference between a function and its inverse. When we graph a function, called $f(x)$, we can watch how each point on the curve flips over the line $y = x$. This flipping creates the inverse function, which we call $f^{-1}(x)$!

2. Determining Inverses:

   • A function has an inverse if it passes something called the Horizontal Line Test. If any horizontal line crosses the graph more than once, then that function does NOT have an inverse. Isn’t that neat?

3. Symmetry:

   • Look for the symmetry around the line $y = x$! This symmetry helps us see how input and output values change places in inverse functions.

Graphs really show us the beauty of inverse functions and make these ideas easier to understand! Keep exploring and having fun with math!