As we study functions
we learn terms like
Input values are the numbers
we put into the function.
They are the x-values.
Output values are the numbers
that come out of the function.
They are the y-values.
Given the function,
we can choose any value we want for x.
Suppose we choose 11.
We can put 11 into the function by substituting for x.
If we wrote down every number we could put in for x and still have the function make sense,
we would have the set of numbers we call the domain of the function.
The domain is the set that contains all the input values for a function.
In our function
is there any number we could not put in for x?
Because we could substitute any real number for x,
we say the domain of the function is the set of real numbers.
To use the symbols of algebra, we could write the domain as
Does that look like a foreign language?
The curly braces
just tell us we have a set of numbers.
The x reminds us
that our set contains x-values.
The colon says,
The symbol that looks like an e
(or a c sticking its tongue out)
says, belongs to . . .
And the cursive, or script, R
is short for the set of real numbers.