Evaluating Rational Functions at a Glance

It doesn't take a lot of heavy mathematical lifting to work through rational functions. We just plug in numbers. That's it—at this stage of the game, anyway. Once we figure out how to calculate the solution of a rational function given a value, we'll become graph-making machines.

Sample Problem

If  find f(0), f(1), and f(2).

To find f(0), which by the way is read "f of 0," we plug 0 in for all the x's in the function.

Which means:

f(0) = 0

Next up, we plug in x = 1 to find f(1).

Finally, we track down f(2).

Sample Problem

If  find f(-3), f(-2), and f(-1).

If you're in the mood to go negative, you can, and you can have fun with it. Here's how to evaluate rational functions for negative numbers.

Which means:

How 'bout f(-2)?

Yep, that's how it's done. Lastly, we find f(-1).

...which means it's undefined at that value. Dividing by 0 is the ultimate no-no.

Sample Problem

If  find f(-2), f(-1), and f(2).

Let's start with the negatives. You're up, f(-2).

Onward to f(-1), which tells us to plug in x = -1.

...which means it's undefined. Boo. And finally, f(2) gets a chance to shine.