[ back to MATH 102/03 home ] | revised 2001-10-14 |

Copyright © 2001 Stan Brown

An earlier document told you how to graph functions wth the TI-83. Once you have a function graphed, you can show its inverse automatically.

For purposes of illustration, let's use this function:

f(x) = sqrt(x-5)

You know from your algebra work that the inverse is

f^{-1}(x) = x²+5, x >= 0

Graph the original function f as `y1`

, using
the techniques you already know.

To graph the inverse,

Press

`[2nd] [DRAW]`

-- look for`DRAW`

above the`[PRGM]`

button in the middle of the black keys.You want

`DrawInv`

, which is menu selection 8, so either press`[8]`

or scroll down to that selection and press`[ENTER]`

. That pastes the comamnd`DrawInv`

to your home screen.Now you have to tell the TI-83 which function you want the inverse of, namely

`Y1`

. To paste`Y1`

to the home screen, press`[VARS] [>] [1]`

to bring up the y list, then`[1]`

to select`Y1`

. Your home screen should now have the command`DrawInv Y1`

.Press

`[ENTER]`

to execute the command. The graph screen will appear and the Ti-83 will draw the inverse function.

Unfortunately, all you can do with the inverse is look at it. You can't trace or do other things.

But at least you can use it to check
your work. For instance, you see that the inverse of our sample
function appears only in the positive *x* region. The inverse
you calculated algebraically, x²+5, has a domain in both the
positive and negative reals, but from drawing the inverse on the TI-83
you can see that you need to restrict the inverse function's domain to
match teh restricted range of the original function.