at first, I would have thought that he had made a mistake when he said that the domain of f(x)=1/x is all real numbers.. cuz I was sure that zero cannot be put because it would be undefined, but then he found out and im like SNAP……… :)))

is answer 2 correct? if somebody stays for 4/5's of an hour, do they get charged $25 (ie a minimum charge of 25 dollars for less than an hour?) they should get a base charge of $15 and a proportional amount for the amount of time 3/5 > 1 for the first hour. as it stands the minimum charge is $15 for less than 3/5 or $25 dollars for anything more; up to an hour. Thanks for the video btw, they're awesome 🙂

For question 2, I'm trying understand the logic behind this. If Maria charges 15 dollars minimum that would mean that M(h) = 15 0<= h <1 since she charges 15 dollars until an hour has been reached, right?

. . . I still don't get it. Everything went in one ear and out the other. Can someone else explain it to me? Like, try explaining it to me like your explaining it to a 10 yr old, please.

How do you get the range of a rational function whose numerator and denominator are both in quadratic form? Without using a calculator how do you get the range?

What does 0 have to do with the first one?? I'm just dumb 😭😭😭🙁🙁. Of course he doesn't work 0 hours but what does it have to do with Duntin charging $10 per hour.

This was amazing! Was able to understand each and every bit of domain and range now. Thanks so much Khan Academy! And for those peeps who don't understand this, you need to go and learn what functions are first. These are basics you need to master

Well i think you teach really very well, i wish you were my teacher cuz my teacher said that it's too complicated for you kids so just memorize it and bcz of him now i hate maths but if you would've been my teacher i would be an expert by now😄😄👌👌

In number 2, should the condition for $15 be 0<h<=3/5?? Since you will not get paid if you work 0 hour regardless of the given situation. Please let me know if I'm correct or not , I would appreciate the answer😊

## 100 Comments

## Dan Tomazin

why 27 dislikes, so many haters out there!

## Hugh Mungus

This guy is so helpful, helped me through my A-Levels and I can actually learn maths. Thank you, and keep up the good work

## Juan -

Sal just got me through my algebra 2 test. Best math videos ever

## Zac Schneider

Thanks a lot – really helped me out.

"A really positive number"… hahaha. =)

## Jen Newell

omg

## Jen Newell

I am so glad that Jason and Khan Academy has put this all online since the college I go to sold me the wrong book twice, Thank you

## Fedel Caracut

at first, I would have thought that he had made a mistake when he said that the domain of f(x)=1/x is all real numbers.. cuz I was sure that zero cannot be put because it would be undefined, but then he found out and im like SNAP……… :)))

## Enderpearl GT

At number 5 the domain should be all real numbers unequal to 0.

Edit: nvm i was panicking early and typed before he saw his mistake

## Seth McMuffin

41 dislikes? haters gonna hate!!

## Ghandy kozman

i thought a function can not have 2 answers? as in one domain can not have two ranges?

## christian n

for question 2:

shouldnt Domain= h =or> 3/5

## float

is answer 2 correct? if somebody stays for 4/5's of an hour, do they get charged $25 (ie a minimum charge of 25 dollars for less than an hour?) they should get a base charge of $15 and a proportional amount for the amount of time 3/5 > 1 for the first hour. as it stands the minimum charge is $15 for less than 3/5 or $25 dollars for anything more; up to an hour. Thanks for the video btw, they're awesome 🙂

## float

Question 5: would the range be equal to or less than 1 seems x is the denominator?

## tdstudent1

lol how much he uses cute

## TheUltimateWaifu

For question 2, I'm trying understand the logic behind this. If Maria charges 15 dollars minimum that would mean that M(h) = 15 0<= h <1 since she charges 15 dollars until an hour has been reached, right?

## Elin Jang

What is y=x squared minus 5?? Please answer!!

## Uhh Hhhh

I was sick yesterday and now my teacher refuses to help me review or show me the notes so yeah…

## Michelle Wanha

Thanks Khan!

## karan bhatia

Namaste very good excellent job

## axel rod

i still dont get it

sal u neeed to explain it to me like im a five year old or something

## axel rod

anyone out there

## Mercy Garcia

. . . I still don't get it. Everything went in one ear and out the other. Can someone else explain it to me? Like, try explaining it to me like your explaining it to a 10 yr old, please.

## Kevin Huynh

3:07 what's the symbol for rational numbers?

## Angel Estrada

You're a terrible teacher you confused me even more!

## alexy lexi

I can't see the problems sighs and I literally hunt your videos…

## Phil Cabilla

Delete your video please

## Aleona Juntilla

I can't still get this right. Oh gosh

## kelvin ngunjiri

Still dont get diffrence of range and domain

## ALowlyEngineer

I have been through the entire of Calculus 1 and 2. Still manage to forget this 😅

## S.D.N. S

This might as well be a foreign language. This makes no sense😩

## Crs-10

I don't get how people do not get this math. Its basically learning something like chemistry, physics…

## Soviet Ivan

TTTTTTTHHHHHHHIIIIIIIISSSSSSSS. iIIIIIISSSSSSS. SSSSSSSSPPPPAAAAARRRRTTTTTTAAAAA. ,!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!L!!!!!!!

## chai

Idk why but I seem to be able to not focus in class since my teacher is so monotone.. I just need something like this to help me comprehend so thanks

## Lil Tylenol

ima cry

## Er mohammad safique

nkich

## Unknown

Thank you

## josh lerio

Now how would you work with infinity when it comes to domain and range?

That's what I'm confused about.

## eva t

Thaaaank you

## *Liam SpiritBreaker*

Sorry I don't speak math

## eunyou park

Isn't -2^2 =4? Then y does my calculator read -4

## A'n'B Gaming

Wow…You are much better than my tuition teacher…

## Wicked Googly

I'm studying for an entrance exam into grad school and I can't even do this shit…

## Andy E

Is domain and range simply input and output, respectively? Why are they called domain and range?

## Claire Cuthbertson

Thanks really appreciate it

## ピントPinto

ima be tellin the truth. this is way better than goin to tutering after school!!!

## michael jordan

this is hard

## ferleal24

8:07 That's what she said

(I'm so sorry)

## noobmaster69

What! Maria is so greedy. My maths tutor charged $15.5 a month, averaging 15-17 hours a month

## Avlon Kuraji

I can't see it ,_,

## Lucozadee

This is a terrible video, all the examples have domains of pretty much anything. What use is that? Need examples of other types! Disliked

## Ben Blevis

The problem with Khan Academy is the pacing it also goes at a too slow pace.

## Leslie Sifuentes

It's so hard

## RobTheNikeHead

you teach this so easy and understandable, meanwhile it sounds like my professors speak another language when they teach this

## FATTY D' food lover

i'm not sure but the domain in no. 3 is (-12,+ infinity)

## Quackin Panda

So many mixed comments saying it's confusing or absolutely amazing. WHICH ONE IS IT AAHHH

## amin quraishi

your way of teaching makes me sick

## Gabriel Cosgrove

But both the domain and the range need to be inequalities…? Not just cop out and say "all real numbers"… Right…?

## Joshua Koh

8:27

## Kohis Negere

This was the best explanation I ever searched. Thanks very much

## Badiyya Suleiman

i love khan academy they teach me lots of maths THANKS!

## Prashant Ghimire

For question 4, why can't the domain be lower than 5?

## Nick Metz

why am i so confused

## Ivan Mideros

I don't understand

## Collin Rodgers

Who needs a math tutor when you have Khan?

## Sam Cadderito

Couldn't have explained that better

## Usman Khan

Can someone explain How Domain & range are Written in sets Like form

Like domain: R-[-2,2)

I would appreciate it if someone would help me out

## faz relf

KFUPM

## Sayedur Rahman

Aswm sir

## Dominic Stanley

Stop saying cute

## Jazz Day

Good video, but why do you say cute so much?

## Jorge Picco

Marvelous explanation. Example number one gave me a practical view, just what I needed.

## Jenna Bk

I HATE FUNCTIONS! They make it complicated for no fkn reason!!!

## James E

How cute

## A Ray

why cant we put complex nors in functions?

## Moeed555

When he says as a function of ….. it confuses me

## Jack Price

bruh

## Nouman Khan

Sir how to find the range of x^2-9/x-3

## Horcrux Gaming

9:22 "There's no way to get zero"

Audrey Hepburn calls in the background, "nothing is impossible.."

## Jefferson Giann Ebal

How do you get the range of a rational function whose numerator and denominator are both in quadratic form? Without using a calculator how do you get the range?

## Andrew Anane

What does 0 have to do with the first one?? I'm just dumb 😭😭😭🙁🙁. Of course he doesn't work 0 hours but what does it have to do with Duntin charging $10 per hour.

## moonlight burn

I hate 8th grade

## Monica Thompson

Yaaaaaaaaaawwwwwwwwwnnnnnnnnnnnnnnnnnnnnnn😞😞😞😞😞😞😑😑😑😑😑😑😴😴😴😴😴😴😴

## Dinesh kumar

Good job 👍 tysm

## Bree

What if you had y=x^2 ad you had to find the domain and range of just that equation.

## Evan Landreneau

Lol I'm so dumb I can't understand this.

## Mimi Schaefer

I’ve come to the conclusion that I am stupid. Math does not make one ounce of sense to me

## dingaling in my butt

The 226 dislikes are those who don't understand this, one of those may be me.

## Alex Voxel

This was really useful, thank you!

## Omar Sherief

Question no. 5: can I say that the range is smaller than or equal 1 because it will never be bigger than 1 actually cuz this is a fraction?.

## Lolz Roll

I'm confused help

## Chase Louie

Thank you so much!! This is so helpful for me.

## GameOnBeast

This was amazing! Was able to understand each and every bit of domain and range now. Thanks so much Khan Academy!

And for those peeps who don't understand this, you need to go and learn what functions are first. These are basics you need to master

## Peter

You explained 90% of the concept in the first few seconds of the video

## Alina Minhas

Well i think you teach really very well, i wish you were my teacher cuz my teacher said that it's too complicated for you kids so just memorize it and bcz of him now i hate maths but if you would've been my teacher i would be an expert by now😄😄👌👌

## ATEhao

Sir you are really confusing us with so many operations

## April Acevedo

you explained it better than my teacher

## mika paguyo

I feel so bad because I still don't understand huhuhuhuhu.

## Jayparkash Jayswal

Really ,this is so helpful

## layek

Just because a guy helped me for my exam without any fees, I'm gonna teach kids for free.

## Yam Alduñar

In number 2, should the condition for $15 be 0<h<=3/5?? Since you will not get paid if you work 0 hour regardless of the given situation. Please let me know if I'm correct or not , I would appreciate the answer😊