Understand Domain and Range

Understand the domain and range of a function. The domain is the set of all values that can be input into a function and the respective output values are the range. There are restriction to the domain in terms of the real number system which the video will explain.

[@bobdane5318]

Who came here because theres a test tommorow and your teacher doesnt know how to teach

[@annshouldsleep]

I'm in the same predicament!

[@AR-nq6wy]

Me

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If it's tomorrow, why study last minute?

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i came here on my own interest

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I wanted to first give God the praise for allowing me to find you on youtube. I am 44 yrs old and have not been in school in over 20 yrs. I was having trouble trying to get my high school diploma at the beginning of the year and could NOT pass geometry. I decided to go for my GED instead at the end of last month. Math was my biggest obstacle until I found your channel. You take the time to breakdown every step of the equations no matter what lesson it was. I took my math GED test today and passed after studying and practicing with your videos and website for the last 10 days. THANK YOU, THANK YOU, THANK YOU.

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If you liked this guy. You would also like the KZbin Channel, Mathantics. Which you probably already know

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congrats!

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My teacher: 复制和粘贴 This guy: 1+1=2

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Teaching face to face Vs. Teaching in youtube in a nutshell

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He still saying moon runes to me

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"If you're watching this video, you're probably in Algebra 1" Me taking Algebra 2: 👁️👄👁️

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same 😂🖐️

[@MsHeavenlySmile]

Sometimes you just have that lesson and after a Week or 2 I'll suddenly fall out

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me taking pre calculus in college, already after taking college algebra T_T

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Set playback speed to 1.25. You can thank me later

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2x for me

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Thank you nick

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You will be my dad now

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actual g

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[@kindbarcid8195]

Cuz there isn’t enough

[@kindbarcid8195]

I have to do this in 7th grade

[@marilynmiller4391]

This video has a couple of errors. Check some other sources such as Purplemath.com and PatrickJMT on youtube.

[@tati.5664]

@@kindbarcid8195 me too .

[@kylagonzales1723]

Sometimes your prejudice for your teachers affects your attitude and attention inside the class. KZbinrs give you directly the information that you need while classroom teachers ideally "facilitates" learner centered activities to help you learn the skill on your own. In that way whatever you learn will have a higher possibility of being retained. However, these kinds of videos are really helpful especially for students who need more time understanding a concept that cannot be given enough attention inside normal classroom setting where students mathematical abilities and pace vary. I hope you will still see the efforts your teachers put into their work to not just earn money but to help young ones develop holistically.

[@SS-yg1yo]

Excellent explanation. Thank you for it. Million times clearer than my son's math textbook!

[@leafpelt2624]

I was scrolling around when I found this video, which seemed to be about the part of math I needed to study for. It was and even as a not native English speaker I understood it and it helped me greatly, thanks!

[@ginadeleon3768]

Very easy to follow. I like how its simplified. I don’t speak math so this language lesson helped me to understand. Stick with the lay terms concept. It worked great for me. Thank you. The whole machine and breaking it just really helped Thank you!!!!!

[@PASTORMATTHEWTAIWOAKINLALU]

❤

[@victoroluwabiyi7527]

Thank you very much. I've been trying to understand this for sometime now but once I watched this video, all question were answered.

[@thevminist]

Came here because I don't understand my teacher. :/

[@annarodriguez9457]

Minhee 😍😍😍😍

[@JuniorRangerClara]

Preach!

[@piaabonal231]

Same

[@mrs.Hedgehog01]

Same lmao

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Stan alert

[@mboadiboadi3552]

My true humility to your explanations that are broken down and gentle to be able to comprehend. I am in the midst of learning this topic over the weekend to finish it fully. Thank you❤️❤️

[@marilynmiller4391]

** VIEWER BE WARNED: Overall, useful video. There are some errors that need correction. First, for y= sqrt(x). Mathematical notation has the rule (i.e. writing convention used in mathematics) that the radicand itself represents the POSITIVE square root of your domain element; NOT both roots. If you mean both roots, your equation would have the "plus or minus" symbols preceding the radicand, (and as described in a later sentence, would violate the definition of function altogether.) Therefore, the range of y = sqrt (x) is the set of all numbers greater than or equal to zero. A graph of the basic function corresponding to your equation will confirm this. Another thing to note is that IF you mean the radical function with index 2 that actually WOULD include both roots, the graph of that shows that the graph fails the Vertical Line Test AND the relation format shows that this gives you TWO distinct ordered pairs with the same first element. So, including BOTH roots in what was written says that the example used would not even satisfy the definition TO BE a function. Yes, there is still a "domain" in the sense of input; however, it is not the domain of a FUNCTION. Second, for x squared +2; the range is NOT all real numbers; rather, it is the set of all real numbers greater than or equal to 2. The function is that of a parabola with vertex at the point (0,2) i.e. the "basic" or "parent" quadratic function with a vertical shift up 2 units. (Review linear transformations of functions.) y=2 is the minimum y value because this parabola opens up. Again, this can be verified with the graphing calculator. These facts that I have stated can also be shown in any textbook covering Algebra I (Math I ), as that course covers both of these relatively simple functions. I had planned to send the link for this video to my College Precalc students for review purposes. Luckily, I previewed the entire video before doing so. And those of you who come here because your "teacher doesn't know how to teach" need to be aware that videos such as these are quite useful; sometimes your teacher DOES know what s/he is talking about. Take ownership of your learning so that you don't need to rely solely on an instructor. And remember that not everything you find online is necessarily accurate. You should use videos such as these as reviews, and understand that if anything disagrees with what your instructor and textbook say, you need to do additional research and verify what is actually correct. (And, yes, I am absolutely correct on what I have pointed out, so I will not be engaging in any argument on this.) I do hope the author of this video will make corrections (just as Sal Khan has had to do for some of HIS videos), and post a comment on my comment that corrections have been made.

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TLDR

[@lindaginn7714]

@@olliew2932 But she is correct. If you are making the effort to go to the internet to learn something, don't you want to be learning it correctly? She didn't say it was a horrible video. She just pointed out a couple of things to make it an even better video. What's wrong with that?

[@amyb.6582]

Thank you. This is the most helpful, basic video on this subject I have found.

[@Francis-fo2ri]

First 4 minutes and I finally understood it. You made it too easy to understand. Thank you.

[@nicolewisse4536]

i procrastinated learning this and now it’s the summer before 9th grade and i feel the need to finally learn this because i’m stressed that imma need this

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you needed it didnt u

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did you need it

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Rocio Aviles great man any tips???

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I just saw this video in 2024 but it really helped me I now see what’s happening after watching many videos this one is the best

[@stalex35]

I paused this video to say Thank you! You are the first one, who mentioned imaginary numbers while talking about square roots of negative numbers. Everybody else just say "there is no sqr roots of negative numbers" and go on... Again thank you

[@mayrolas1]

hi, that was an excellent way to explain it, it even helps to understand some precalc material, thanks very much.

[@norsauve6160]

Thank you for explaining it in a simple way. The virus has made school hard especially the fact that I’m a 7th grader taking high school algebra. Thank you!

[@JustCaden]

Doesn’t everyone learn algebra in 7th?

[@amani98001]

@@JustCaden it depends whether or not you are in accelerated classes or not (they teach you different things)

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Same but i missed 6th 7th and pre alg cuz of covid but i take alg so i study a lot i have an 86% and it should be like an 87 within the hour i need to get a 100% on my finals

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thanks a lot! my teacher didn't explain this well so I'm glad I found this video

[@rohitchaurasiya7311]

Great explanation. thank you so much for uploading this video

[@evelynfleming8226]

Thank you so much for this video! It completely helped me to understand the concept better, and I appreciate that you used common terms and didn't hit us over the head with a bunch of crazy math mumbo-jumbo. I will probably be using your videos in the future for more math help!

[@sakuramidnight5230]

When u couldnt get into zoom but u have a test and didnt learn this 😄✌

[@dsalinaspk]

Thank you, Thank you, Thank you. Fantastic way to make a old man like me understand.

[@emyrgrznsky9943]

Failed math 101 twice finally up in me arse trying to do something on my own.. i sometimes feel super dumb but i somewhat understood this i guess thank you very much for expecting that some of us might not get this so that you explain it deeper thank you

[@vanillapretzelover]

Thanks so much, I was struggling with this

[@gabrielmchilomo4723]

An excellent explanation 👍 Give us an explanation on the range as well.

[@rodrigolopez4759]

Really helpfull, hundred times easier than what my teacher explainded

[@user-mi9eq5fd8h]

thank you very much This video was very helpful and informative for me. I still didn't know what domain and range mean, but today after watching this video it became very easy to me

[@danielmackic2151]

You saved me my teacher is so terrible and you just made it so easy to understand thank you so much

[@user-zp1ky6mm9g]

This is so helpful more than what my teacher is teaching in class i really understand better here ...thank you sir

[@Optimally_healthy5831]

Thank you, very well explained :)

[@sakuntharanaweera2457]

Crystal clear 👌.. thank you so much sir..❤

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Thanks alot! It was really easy to understand.

[@zuhairalsaffar7001]

I like your way of teaching thank you so much for your help ❤ 😊 🙏

[@ebonyravenhood9843]

I think I understand domain and range now..thank you so much

[@aneshamcdowell3308]

Thanks. You made this easy to understand.

[@ScienceBronzewall]

Thank you so much for the simplified and Explicit explanations. Keep making Learning Fun.

[@eltoona4841]

Thank you Tablet Class, Very Cool!

[@nervi7523]

Great teaching!

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this helps us a lot, thank you.

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is anyone here because your teacher did not teach you your homework

[@legacyfe4r]

This was so helpful thank you!!!

[@ayyahtomawis3043]

thanks for this! i had a hard time solving my assignment

[@mulatuperi746]

Wow ,that's a great explanation. I like it.

[@robertgammett8718]

Domain and Range for whatever reason is the bane of my mathematical knowledge.

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kindly watch this video on youtube -(examination in life and never give up mufti menk by merciful servant )

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Your speaking style dude 👌 awesome 👌 you are dude bro 😎

[@termel140]

I honestly thank you for all this because I absolutely cannot do this myself

[@nhsmath5685]

I appreciate this video so much and it is exactly how I like to teach domain, however, if you can please correct the fact that the range of the square root of x is all numbers greater than or equal to zero. If your function is the square root of x, it is asking for the principal root of x which is only positive outputs or zero. Great video though!!!

[@erinnecoit1071]

Thank you for this comment. I was confused by there being more than one possible outcome- I thought that was breaking the definition of a function- but now I understand.

[@kentkaiser9381]

Is the range for x^2 + 2 really "all real numbers" (as you state at 12:58) or is it "all real numbers greater than or equal to 2"?

[@prabhathsannasooriya]

realy good examples and very clear

[@mathtodaychh132]

The best teacher thanks for sharing

[@venkataratnampadaga3392]

Excellent Sir good explanation to understand differences between domain and range

[@mustafatoppi]

Always get confused between both of them Domain & range thanks a lot Pal

[@Maryam-bs2wd]

You saved me.thankyou.

[@caribaez5711]

i need explanation about interval notation based on domain and range.

[@nyadodd6671]

So much better explained than my teacher

[@augustayarteh7524]

Ya if. F(x) you should set it like this f (2) is representing the x in the parenthesis. Domine is a set of all numbers that you can input into your Data or machine. Nice explanation.

[@tgrant414]

Very helpful in trying to assist my son. Thanks

[@destinyovbiebo8988]

Smart mom

[@Eulalia42]

Very helpful video.

[@uchegideon7190]

The most simplified explanation

[@bricelegendnducho]

This is so fascinating

[@Nyxia-cb2og]

Thank u sooo much it was soo easy to understand

[@imrang3264]

Thanks for your help sir 👍👍👍

[@carolinavargas1852]

In the second example of x^2+2, why is the range the set of all real number if we can get only positive answers? It is because in the domain we could put a complex number (x= (-3^(1/2))? If we define the domain as the set of all real numbers, then is the range still all the real numbers or just the positive ones?

[@brucewayne-ml2fu]

thank you very much bro it helped me so much

[@viciousleo340]

I got a question can u make a video about all the definitions bc I'm trying to study for my GED I wrote everything u said down so I can use it to study your video helped me more then anything else did so thanks💙

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thanks a lot i have enjoyed the lesson for real

[@knuckledragonfly]

I am in school right now earning my last 60 credits in my Major Mathematics. My question is what books would you recommend to help me dive further into this field? I want to learn about fractal geometry and incompleteness theorems

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Did you get any 😉😉

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I came here one hour before my math test after my friend sent screenshots of the actual test.

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Your friend is a real one

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@@BeNothingg facts

[@iceinkfxc8595]

great intro to domain and range

[@user-xi7qb8nd5l]

Thank you so much for going over this. Very well explained. Quick question, why the range of X^2 + 2 is not equal to the set of real numbers greater or equal than 2? Since the square root of a real number will always be at least zero? zero +2 = 2.

[@tarashansda2996]

Satisfied 😀😀😀

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i’m taking a pretest for algebra 2 and completely forgot all this stuff💀

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same, but I got algebra 2 honors

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I subscribed your channel and i liked it

[@amazingsciencebysirjude8558]

may i ask what platform application you are using? just want to try it on my online class, thanks!

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great video, tho all I could think "what is a 'tackulator'" but I heard 'calculator' wrong lol

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Bro really saving lives for free

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Wtf this dude makes me laugh on his machine jokes

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This video from 2006 is helping

[@javanfolkes28]

A good teacher

[@danielgray8053]

Great video but I spot two mistakes let me know if you think I am wrong -- 12:59. T he range of f(x) = x^2 +2 is all real numbers? How would you ever get a negative value for Y? Also, the range of y = sqrt(x) which you mentioned earlier in the video is not all real numbers either. its all POSITIVE real numbers. II don't quite understand this myself. But just take a look at the graph of y = sqrt(x). You can see that the range is definitely only the positive real numbers. Good teaching style. I came to watch this to give me an idea of how I was going to teach domain and range to a student of mine and you definitely gave me some good ideas

[@danielgray8053]

AHh a commenter below totally said all this already albeit in much more concrete terms

[@helentolu3502]

Nice video!

[@cliffordbliss5578]

You are the best

[@mikeykim2823]

Thank you for the video! but I have one question. You said that square root of 16 is +4 and -4. But isn't it only +4?? How can it be also -4? 10:57

[@alikadawany174]

In the example before last the range should be just the potive numbers, yes?

[@arcacia9280]

thx for the video, it's super

[@ammiepama1513]

I didn't do maths in high school..now I'm studying Information Technology at Varsity and I have no clue of functions ..infact anything to do with maths😭

[@marilynmiller4391]

Try Purplemath.com and Patrick JMT youtube videos

[@uruonyemaobi1950]

Jesus lol, I thought I was going to study Law now i'm studying International Business. This mathematics ting is beyond me lol

[@henryluo902]

@@uruonyemaobi1950 how’s international business going for ya?

[@kaihayes2710]

I have finals today, im cramming right now

[@NeilSharks]

Nice video. I dozed off 3 times

[@AnkaraMessi635]

Thank you so much!

[@MrLoop-wz2sb]

thanks a lot sir.

[@alhamduliah1510]

Can you explain more about me?non- uniform function