Evaluating Functions

This lesson will make extensive use of the basic terminology and notation for functions. If you need a review of this information, click here.

The notation

means that we have a function named f and the variable in that function is x. The domain of the function describes values of x that can be put into the function. For example, if we want to put in a value of 2 into a function, we would be letting x = 2 in the function. Our notation for that is . Let’s use this in a function.

1. If , find .

The notation

means that everywhere we see x in the function, we are going to replace it with 2. This gives

Our notation is

Notice that it is not absolutely necessary to enclose the “2” in parentheses, but if functions are more complicated it is helpful to avoid confusion.

2. Let . Find and .

To find

we will substitute -1 into the function everywhere there is an x. This will give us

Our notation is

We use a similar process to find

to find

When evaluating functions, we may not always be asked to evaluate the function at a particular numerical value.

3. Let . Find and .

Although we are now asked to work with variables instead of numbers, the process is exactly the same. To find , everywhere we see an x, we substitute the letter b. Likewise, to find , substitute

the entire quantity everywhere there is an x.