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) = −4x2 + 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.