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Domain and Range
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R, the set of real numbers.

So we read it, The set

of x

such that

x belongs to

Slide 17

When we put 11 in for x,

When we put 11 in for x,

y was 17.

Slide 18

So 17 belongs to

So 17 belongs to

the range of the function,

Is there any number that

we could not get for y by

putting some number in for x?

Slide 19

No!

No!

We say that the range of

the function is

the set of real numbers.

Slide 20

The set of y, such that

The set of y, such that

y belongs to R,

the set of real numbers.

Read this:

Slide 21

the domain and range

the domain and range

can be any real number.

It is not always true that

Sometimes mathematicians

want to study a function over

a limited domain.

Slide 22

the function

the function

They might think about

where x is between 3 and 3.

It could be written,

Slide 23

limits the domain or range.

limits the domain or range.

Sometimes the function itself

In this function,

can x be any real number?

Slide 24

were 3?

were 3?

What would happen if x

Then we would have to divide by 0.

We can never divide by 0.

Slide 25

3 from the domain.

3 from the domain.

So we would have to eliminate

The domain would be,

Slide 26

which could not belong to the range?

which could not belong to the range?

Can you think of a number

y could never be 0.

Why?

Slide 27

There is no number we can divide 1 by to get 0, so 0 cannot belong to the range.

There is no number we can divide 1 by to get 0, so 0 cannot belong to the range.

for y to be 0?

What would x have to be

The range of the function is,

Slide 28

that limit the domain of functions are:

that limit the domain of functions are:

The most common rules of algebra

Rule 1: You cant divide by 0.

Slide 29

of Rule 1: You cant divide by 0.

of Rule 1: You cant divide by 0.

Weve already seen an example

Slide 30

You cant take the square root of a negative number.

You cant take the square root of a negative number.

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