Drawing Inverse Functions on the TI-83/84

Summary:  After you graph a function on your TI-83/84, you can make a picture of its inverse by using the DrawInv command on the DRAW menu.

Let’s use the function , shown at right. (If you don’t know how to graph a function, please review that procedure.) My window margins are 0 to 10 in the x direction and 0 to 6.5 in the y direction.

Since the graph of an inverse function is a mirror image of the original, through the line y=x, I have also drawn in y=x.

To draw the inverse of that function:

The result is shown at right.

You know from your algebra work that the inverse of

is

f^-1(x) = x²+2, x ≥ 0

and the graph confirms that. Look at points (0,2), (1,3), and (2,6) on the graph of the inverse.

Unfortunately, all you can do with the inverse is look at it. You can’t trace or do other things. But even that helps you check your work. For instance, you see that the inverse of the sample function appears only in the positive x region. The inverse you calculate algebraically, x²+2, has a domain in both the positive and negative reals, but from drawing the inverse on the TI-83/84 you can see that you need to restrict the inverse function’s domain to match the restricted range of the original function.

There’s another way you can check your work. Find the inverse function first, algebraically, and graph it as Y3 when you graph the original as Y1. If you do that, DrawInv Y1 will exactly overlay the graph of your algebraic inverse.

Caution: Because the screen resolution is low, two different functions sometimes look the same. This method isn’t an absolute guarantee that your work is correct, but it’s better than no check at all.