Evaluating rational functions is just
like evaluating polynomials. To keep
it interesting, though (and because you'll need to learn it
eventually, and because this is the section about functions), I'm
using *function notation*. A function tells you what to do
to an input to produce an output. Functions can have any name, but
the most common name is *f*. Then *f*(1) means
“the output of the *f* function when the input is
1”. (In the notation of the section
about functions and relations, it's the second member of the
ordered pair whose first member is 1.) To know what that is, you
need to know what *f* does. For example, your teacher might
tell you that *f*(*x*) = −4*x*^{2}
+ *x*. Then *f*(1) = −4(1)^{2} + 1 =
−3. In general, whatever letter is in the parentheses in
the definition of the function, you want to plug in 1 for that
letter in the formula on the right-hand side.

In this example, *f* was a polynomial function. It would
work the same with a rational function, or any other kind.

Please note that *f*(1) *does not* mean to
multiply *f* by 1. Yes, it's a confusing notation, but it's
the one we're stuck with.