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. 
