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As we study functions

we learn terms like

input values

and

output values.

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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.

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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.

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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.

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The domain is the set that contains all the input values for a function.

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In our function

is there any number we could not put in for x?

No!

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Because we could substitute any real number for x,

we say the domain of the function is the set of real numbers.

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To use the symbols of algebra, we could write the domain as

Does that look like a foreign language?

Let’s translate:

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The curly braces

just tell us we have a set of numbers.

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The x reminds us

that our set contains x-values.

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The colon says,

such that

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The symbol that looks like an e

(or a c sticking its tongue out)

says, belongs to . . .

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And the cursive, or script, R

is short for the set of real numbers.

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