Determine the domain and range

for the relation described by the table. And so what they

want us to say, what they want us to figure out,

when they say the domain, they’re saying, what are all

of the possible inputs that we could put into– in

this case, a relation, and later we’ll see into

functions– and so over here– or I guess one way

to think about it– what are all of the inputs

that this relationship is defined for? And so you can view

the x as the input. So when x is negative 1, y is 3. When x is 3, y is negative 2. When x is 3 again, now y is 2. And that’s why we can’t

describe this as a function here, because we have two

different y values for a given x value, but it

can be a relation. When x is 4, y is 8. When x is 6, y is negative 1. So to answer the

first part, when they ask us what is the domain

of this relation, they’re really just saying,

what are all the inputs? What are all the x values for

which this relation is defined? And they list the x

values right over here. So it is the set– and that’s

what these curly brackets mean that I’m about to

describe a set– it is a set of the numbers,

negative 1, 3, 4, and 6. So all we’re saying

here is if we say the domain of this

relation is these four numbers, it says that this

relation is defined for any of these four numbers. If you give any of these

four numbers as an x value, there is a y, at least one

y value, associated with it. Now, when they talk about

the range of this relation– and the idea also

applies to functions, which are a more specific

class of relations. You can view them as a

well-behaved relation. The range is, what are

all the possible outputs that this relation can give you? Or given the inputs, what are

all of the possible values that this relation can take on? So here you’ll take a look at

all of the possible y values that it can take on. So we can get– and I’ll write–

we could write them in order or we don’t have to

write them in order, but I’ll write them in order

just for the sake of it. Actually, let’s just

go straight this way. It doesn’t have to be in order. A set does not imply

some type of order. It just means a

collection of things. So the range here, well, our y

value can take on the value 3. It can take on the

value negative 2. It can take on the value 2. It can take on the value 8. And it can take on

the value negative 1. And we’re done. These are the x values for

which this relation is defined that you can actually find an

association or relationship. And these are all the y values. These are all of the outputs of

the relation that it can take on, and we just looked right

over here to find them.

## 22 Comments

## M T

First ðŸ˜€

## Faerhad Targaryen

Iuguihguudxv

## lolomgdude

@Supacalaz

In Stats, it's Max-Min. In Algebra it's the Y-value.

## chrisnnuzz

its britney bitch

## Darius Banks

thx

## Whitewash808

Did not help my problem at all.

## Vigorous

This helped a lot since I'm learning Common Core Math which is a new way of teaching math in Ohio.

## Caleb Harmon

Damn this is a lot easier than I was making it

## Ahmed

So helpful! Thanks so much.

## Ghadeer Ali

Omg thank you so much! My teacher sucks at teaching so this is very helpful ðŸ™‚

## robert webb

Thanks I can't believe I forgot this

## akanksha Pawar

very useful

## Siti Mudrika Zein

how if R = { (1,2), (1,3), (2,3), (2,4), (3,1), (3,4) } is it Transitive

or not ? i'm not sure about my answer because it has the variable which

has transitive function such as (1,2), (2,3) = (1,3) E R but it has

(1,3), (3,1) then (1,1) and its not in the R ? please help me! big thanks

## X Lence

fuck math fucking evil piece of shit. depressing the hell out of me ðŸ˜

## Marwah Ghouli

Thank you so much, I was absent in school and this helped me catch up really quickly. Thank yoouuuuuu

## Dark Orbit

Thank you so very very much I finally understand this now

## Collin Hull

I'm thinking about becoming a math freak

## Sturtevant Rail Productions

thanks very helpful

## Edward Leo

what if the relation is in equation form?

## N/A N/A

i hate math, but this channel makes it easy, and i have a much better experience

## Dre Jr.

thanks I was making it harder than it was

## Kurt Cobain

What if they have I.e.

3|8

4|8

3|4

Would you put 2 of the same or what