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.

**Let's Practice:**- 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.

- 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.

- 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*.