Hi everyone!

Today we’re going to talk about how to find coordinate points and the domain and range

of a function just by looking at the graph of a function. To complete this problem, we’ll

look for points on the y axis that correspond with points on the x axis then, to find domain

and range, we’ll look for all x and y values that the function attains.

Let’s take a look. And in this particular problem, we’ve been

asked to find f of one and f of five, as well as the domain and range, based on the graph

of the function. So, the first part of finding f of one of

five is just interpreting values from the graph. When we’re asked to find f of one

and f of five, all we’ll be doing is looking at the y value for the function when x is

equal to one and five. So, for example, f of one, we can locate the point on the x axis

where x equals one, so that’s this point right here, and to find the corresponding

y value, we just go up and meet the graph wherever it is and we see that we get to the

graph of this point, if we go over to the left, we see that we have the y axis at three

right here so we know that f of one is equal to three, and this basically means that we

have the coordinate point (one, three), where x is one and y is three, on the graph of our

function. So, same thing here with f of five, we find the point along the x axis where x

is equal to five and we go down in this case to meet our function. So, we come down here

to meet our function and if we come back over to the y axis, we see that we run into approximately

negative two. I haven’t drawn this graph perfectly but the idea is we run into negative

two here on the y axis so we get negative two for f of five. And, that tells us that

we have a coordinate point on our… on the graph of our function of (five, negative two).

That means that when we plug in five to our function, we’ll get back a value of negative

two, or when we plug in one to our function, we’ll get back a value of three.

So now, when we talk about domain and range, we wanted to find that domain is all of the

x values for which the function is defined. So we just need to give a list or a range

of all x values that this function could possibly attain. And if we look at the graph of this

function here, we can see that the smallest x value it attains is x equals zero, right.

There are no x values to the left of this point for which the function is defined. This

is where the function starts on the left hand side; it ends here on the right hand side.

So we know that the domain runs from this point all the way to this point and the left

hand side here is equal to zero, the right hand side is equal to seven. So we can say

that the domain is x greater than or equal to zero and less than or equal to seven. We

can also write that as in square brackets like this, [zero, seven].

Now, the range is the corresponding set of y values that the function can attain based

on the domain that we’ve already defined. So, on this… on this domain here from zero

to seven, which y values can the function attain? Well, we can see here that… (we’ll

use a different color) we can see here that the highest y value is at this point here

and that the lowest y value is at this point here so we know that our range runs from this

point to this point, that’s the range. The y coordinate at the top of our range here

is four and at the bottom, it’s negative two, so we can say that the range is y greater

than or equal negative two and less than or equal to four, and, again, we can write that

as negative two to four. And that’s all there is to it. That’s

how you can find coordinate points or values from your function, and domain and range from

your function, just by looking at the graph of the function even when you don’t have

the function’s equation. So, I hope you found this video helpful. If

you did, like this video down below and subscribe to be notified on future videos.

## 71 Comments

## Krista King

you're welcome!! 🙂

## Usman Hari

You are the most wonderful thing i have ever seen i my life, You are the definition of beauty ,.

## Krista King

awwww thank you!! 🙂

## macracwhite

Silly to ask but at 2:02 can't we point out the +ve value of 2. It would not be exact 2, but it will be 2 point something i.e. 2.5 or 2.3 like that….can't it happen…

## Ashley

thanks so much <3 all of the other videos i watched were not this helpful!! you deserve way more views!

## Krista King

awww thank you so much!! 🙂

## Tyson Brennan

Hey, i'm still a little hazy on how you got the domain and range :/

## Cheryl myers

how do you determine whether to use parenthesis or brackets

## Krista King

you should use ( and ) by default. if you've already used those, and you need to wrap them in a second set of brackets, then you should use [], like this [ ( ) ] If you need three sets of brackets to define your function, then you use curly brackets, like this { [ ( ) ] }. hope that helps!! 🙂

## Otis Baker

You are great and you've helped me so much! Thank you.

## Krista King

You are so welcome! I'm glad I can help. 🙂

## alfred gondwe

hey thanks for the lessons I love the way you explain you are so clear and straight forward.

## Krista King

I'm so glad you feel that way! 🙂

## Take Temate

Thanks

## Krista King

You're welcome!

## Sammyboy630

You are better than my hon algebra teacher! XD

## Daniel Zuñiga

I jack off to ur face

## Kirk Sr

Thank you your videos have been so helpful

## Krista King

Awesome! I'm so glad I can help! 🙂

## Riniecia Solomon

i am still confused.. the way you do it looks so hard 🙁 is there a easier way ?

## Todd Yo mom

hott. I mean ummm, *ahem* intellectually stimulating.

## Scott T

Your teaching was very demonstrative and easy to understand. Thank you!!!

## Meary gunners

awesome video MS………………..

## Hernan Negrete

Thank you! I have a test in a week and this will help a lot 🙂

## Skyline Busta

this helped, but why do you look like you got punched in the face?

## Everett Borislow

This is interesting. Thanks for helping everyone in math.

## kyle ursu

You are very easy to understand… Lots of people try to over-complicate concepts but you tend to paint them back and white which makes it very easy to grasp the concept you are trying to get across. 🙂

## Mushi H.

What if on my graph the domain of 1 has two lines on it. One starting at y=3 and other starting at y= -2.5. Do i write both of them down or what? Plz reply ASAP i gotta turn this in tomorrow.

## TheKgar

This was great and I found this helpful. Also you seem like a very sweet person to expend yourself for others.

Thank you kind stranger!

## Matthew James

Excellent video thanks!

Where did you find that picture of the blackboard!?

## Mohammed S

Excellent work! I'm having my provincial next week and this really helped me understand the concept of finding the domain and range from a graph. Cheers!

## greg l

Great Job! thx and u have my subscription!

## Siddharth Chandel

awesome …… you are a great teacher !!!! thankx krista king .. you cleared my doubts !!!

## Sourb Mahi

Thank you SO MUCH !! Because of your excellence I understood this so much better, I got an A+ on my Math 1 Honors quiz !! (9th grade math )

## hoptheloop

f(x)=x(x-3) between 0<y<1 i'm so confused, i dont have a graph btw, how do i work it out? :S

## Syed Muntazir Mehdi

Hi Krista KingI am your big fan my emailadress is syedmuntazirmehdi0gmail.com .i wanted you to add some topics on derivitive and maxima and minima concepts on youtube iwill be very thankfull to you

## Syed Muntazir Mehdi

I mean on maxima and minima please add some additional videos igot a big trouble in these topics.

## Whelp Kelp

Omg yasss you cleared up a lot of confusing topics in this vid that my math teacher didn't , hopefully I'll pass tomorrow's test 🙂

## karim khan

madam– — excellent– i do not under stand generalised co ordinates in langragian mechanics

## Supernova

In my pre calc course I had such a difficult time understanding the domain and range in a function. This video made it so easy that its difficult not to understand it. Thank you so much!

## dima71387

Are you single? Just curious.

## vrendus522

*notes, the nature of the line drawn on adjacent to the line graph bar, in true genesis, would be symmetrical lineal function, not prescribed if asked by situation.Example a helix, in proportion is a helix as that would happen.This statement said as some may ask the question,"How does the line, if this is a problem by itself, know to make these statement proportions on the graph, if they are not pre-prescribed by a prothanitor.So described in self logic as genesis in design and a-genesis or non-symmetry.I got confused on this.Another term, a-proportionality.

## acewt timer

I do know that brackets are used for this but aren't there cases when parentheses are applied? what makes those two differ? Also do you know how this can apply to solving rational inequalities?

## Özgür TERZİ

Hi.you are best.Iam from turkey ,ı dont know english but ı know math language ,so ı understant ,what you telling us. can you tell me ,which program do you use.its too nice.real blackboard.pls tell me

## R C

Thanks for helping me understand the differences between Domain, Range, and the functions. Helps a lot!! And you're still hotter than Calculus!!

## Kyler Curtis

Thanks soo much!! I was stuck doing my math on these types of problems. It has been a while since I've done these types of equations. 😀

## aana gul

Thanks alot.

## slap14325

The best. You take approximately the same time I need to understand these concepts. Unlike Khan Academy, you do the math much much clear and to the point unlike any other. Thanks a million, ma'am, extremely appreciate everything you do.

## Richard Argueless

Omg, ive been looking up videos to get extra teaching for exams and have literally found myself searching for your vids all the time now! Just followed you. Your basically my math hero now lol thanks!

## montasr hamza

thanx

## Muhammad Ahmad

Which Camera?

## Ali Raza

Hi its me again who couldn't find videos because of hairstyle lol, two weeks back. I have a question, is it possible to get a question in equations like f(1)=3 and f(5)= –2 and they ask for domain and range. do we have to draw a graph first to do that? please let me know as my exam is this Friday and i am really confused and can't find natural domain too. Thank you very much.

## Vegeta Goku

hi Krista. can you explain binomial probability?

## aditya kadpate

Hey,

Please forgive me if this question happens to be too stupid. But, can we figure out what the function is with the help of given graph?

## Jayce Infinite Al'gharhythmns

"Making the simple complicated is commonplace; making the complicated simple, awesomely simple, that's creativity." – Charles Mingus – Gotta say, that's what you do in a nutshell! Thanks so much for these videos!

## hoosna eydatoula

Thank you

## superzayman1

this helped lol

## Tigero Rousteinire

Ooooh!!! I finally got it! Thank you for articulating slowly and being so patient with your audience! ^_^

Too many videos just trample through the numbers expecting us to already understand what's going on.

Subscribed! :3

## Ali alawasheer

thank you ageen your good teacher

## Zak Antoine

This was actually a great help.. It got 2 of my 4 questions done. Thanks!

## Shehwar's Studio

did somebody punch this lady straight in the face ? LMAO

## Juan Ar

You are so awesome:)

## Desi Kalakar

she is quite sexy!

## Extreme Math lover

Nice vedio thanq

## Extreme Math lover

Thank you sister

## Roberto Carlos Fuentes Deltoro

thank sister you spañol

## kayla silva

please be my teacher

## Zadi

Actually her teaching is very excellent and it’s easy to be understood.

## abu zalmai

so much helpfull

## Nolan Kjerstad

your hot

## Allan Lule

Well understood thank u so much.