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Domain and Range
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Slide 1

Domain and Range

Domain and Range

Slide 2

As we study functions

As we study functions

we learn terms like

input values

and

output values.

Slide 3

Input values are the numbers

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.

Slide 4

Given the function,

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.

Slide 5

Domain and Range

Slide 6

If we wrote down every number we could put in for x and still have the function make sense,

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.

Slide 7

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

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

Slide 8

In our function

In our function

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

No!

Slide 9

Because we could substitute any real number for x,

Because we could substitute any real number for x,

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

Slide 10

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

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

Does that look like a foreign language?

Lets translate:

Slide 11

The curly braces

The curly braces

just tell us we have a set of numbers.

Slide 12

The x reminds us

The x reminds us

that our set contains x-values.

Slide 13

The colon says,

The colon says,

such that

Slide 14

The symbol that looks like an e

The symbol that looks like an e

(or a c sticking its tongue out)

says, belongs to . . .

Slide 15

And the cursive, or script, R

And the cursive, or script, R

is short for the set of real numbers.

Slide 16

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