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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.

Let's Practice:
  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.
  1. 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.
  1. 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.



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S Taylor

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