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

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When we put 11 in for x,

y was 17.

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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?

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No!

We say that the range of

the function is

the set of real numbers.

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“The set of y, such that

y belongs to R,

the set of real numbers.”

Read this:

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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.

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the function

They might think about

where x is between –3 and 3.

It could be written,

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limits the domain or range.

Sometimes the function itself

In this function,

can x be any real number?

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were 3?

What would happen if x

Then we would have to divide by 0.

We can never divide by 0.

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3 from the domain.

So we would have to eliminate

The domain would be,

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which could not belong to the range?

Can you think of a number

y could never be 0.

Why?

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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,

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that limit the domain of functions are:

The most common rules of algebra

Rule 1: You can’t divide by 0.

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of Rule 1: You can’t divide by 0.

We’ve already seen an example

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You can’t take the square root of a negative number.