❖ Finding the Domain of a Function - Made Easy! ❖

Finding the Domain of a Function - 4 Complete Examples Using Interval Notation
In this video, I show how to find the domain of a function without graphing, using algebraic methods. We explore the two major restrictions when finding a function’s domain:
Avoiding zeros in the denominator of a fraction.
Ensuring there are no negative numbers under a square root (or any even-powered root) after simplifying.
Throughout the video, I walk you through 4 complete examples, demonstrating how to find the domain step by step. I also explain how to use interval notation to express the domain accurately. This is a must-watch for anyone studying functions or preparing for algebra or precalculus exams.
🔗 Want to see how to find the domain and range using a graph? Check out this related video:
• ❖ Domain and Range of ...
👍 Don’t forget to like, subscribe, and hit the notification bell for more math tutorials and problem-solving strategies! 🔔✨
#DomainOfAFunction #MathTutorial #IntervalNotation #Algebra #Precalculus #FunctionDomain #MathHelp #Mathematics #LearningMath #GraphingFunctions

[@patrickjmt]

Hi all! Please post comments, questions and anything else on your mind in the comment section! While I try to answer as many questions as I can, there are more questions than I can answer by myself so if you are someone who might be able to help, please do so! The community is so much better when everyone is involved and helping each other out. Our strength is our willingness to help each other! Also please feel free to like or dislike the video. Your feedback is always appreciated so that hopefully I can make my future videos the best possible! Thanks and happy studies!

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You spent 12 minutes, and you taught me more than what my teacher could teach me in a semester, and for that thank you.

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[@patrickjmt]

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Thank you!

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[@chancewilson]

Thank you. From a 33yo returning to college.....and I had the fantastic idea to go for Engineering/Applied Mathematics. All help, especially good help, is GREATLY appreciated.

[@rsxshovon]

Great help!! I just started engineering school 10 years after graduating high school. Needed a refresher and your videos are great!! Thanks! Keep up the good work!!

[@KatieGraham]

We watch these vids as our Calc notes, and then do the homework in class. :) Absolutely LOVE it! These are soooo easy to understand, and then when we do the work in class with the teacher there, I know what is going on, and I know what I need help on and need to ask about. :) Thanks soooo much for making these videos! Our entire Calculus class really appreciates them! :)

[@liittlsky]

I just wanted to say thank you so much for your videos! I am taking an online math course and have spent hours studying and reviewing my book and notes and was still having trouble understanding the information! But I watch your videos and it makes perfect since!

[@nyreehinton1767]

I have a test in 1 hour. Thank you for clearing things up.

[@gustavoalamilla7260]

So how was that test that you took two years ago

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Gustavo Alamilla lols

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i want to know too

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Rachel Munoz same

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did you pass

[@kalabagastonn7301]

Thank God for you.. I was struggling with math in high school but this channel helped a lot. I got into medschool and I’m almost graduating. Much appreciation

[@plasmadragon1998]

WoW... i came for your help last year in my calculus class and now i am back here for my engineering basic calculus. THANK YOU

[@sherainnelouisecasinto1621]

thank you so much xD i was having a hard time understanding this from our teacher because he doesnt really do it step by step. he just suddenly get the domain without solving it and showing how he did it.

[@slaypsp]

A million thanks man, you explained what I tried to understand in 2 months in just 11 good minutes. I'm speechless, thanks a lot.

[@ihartTSwift]

You are so awesome for making these. I really appreciate all the help you have given me. Without you, I would not be passing any math classes.

[@sarahholland5980]

Thank you so much! My teacher skipped over half the rules (ex: when to use greater than or equal to zero vs. just greater than) and I was so incredibly confused. I have a quiz tomorrow, but you're a lifesaver! I'm subscribing and will look at some of your other videos for reference! :)

[@weightelk]

Well, thank you... I have a math test on this stuff tomorrow for my precalc honors class and I've forgotten all algebra stuff... So thank you again, my teacher is do bad, but I can learn very quickly from your videos... Thank you again!!! :)

[@justinmccarroll8008]

You sir are a lifesaver. A math god sent from the internet to help the mathematically challenged.

[@FritosOrLays]

Man, just the first two minutes saved my life. This is better than what any math teacher ever taught me.

[@TheCutedark]

Hello Patric..I'm a fan of Maths and I can't decribe how happy I am that I found ur videos. I just want to say that at minute 3:45 u can slove it with this formula: a*x^2+b*x+c=0 sloves x1/2={-b +- (b^2-4*a*c)^1/2} / (2*a) ..in our case is x1/2={-(-1) +-(1^2-4*1*(-6))^1/2} / 2*1 x1/2=(1+-5)/2 x1=(1+5)/2=6/2=3 and x2=(1-5)/2=-4/2=-2 I don't know if u knew it but with this formula u can slove every quadratic equation.

[@BonafiedReaper]

Thank you immensely you have helped me pass my Pre-Cal final and succeed in life as a result. And no need to appologise so much

[@manto9034]

THNX FOR BEING THE BEST TEACHER/TUTOR EVER!!! You've just helped another person with his Exam... ME!

[@xAreuto]

My teachers couldn't believe that I learned to do this in 11 minutes after they tried to teach me in 3 days. Thx man!

[@anthonybyork]

I am pretty good when it comes to math in general. I really enjoy how you do your videos. I seems pretty straight forward. I enjoy being refreshed in Math.

[@chattinitup418]

seriously this is absolutely saving me on my math test. i was lost in this class without these videos! THANK YOU

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dude you're a beast. i have a college algebra test in a couple days and i plan to just watch your videos.

[@asandmire10]

Very! Very! Helpful. You explain everything in a way that makes it so easy and simple to understand. Im taking AP Calc AP Stat and AP physics this year and im going to use many of your videos to help me

[@patrickjmt]

@genemalu well, to draw a pretty accurate graph you can use calculus. otherwise, u just gotta plot some points and/or think about the function!

[@lilque0000]

Whoa!!! This is Amazing i only watched your video for 3 minutes and learned how to do something that would've take 30 minutes in class. Thank you so much! I am now Subscribed to You!

[@amandad1419]

You NEED to become a math teacher! You are so much better than 95% of the teachers I've had.

[@jazzmanjunior]

Patrick you're helping me out very much and i want to thank you. My preCal teacher isn't very good so your tutorials are life saviors! Thank You! :D

[@patrickjmt]

@chloetan2912 you are using set notation, i think i use interval notation. it is all the same thing, perhaps just ask your teacher if they have a preferred notation for you to use.

[@patrickjmt]

@tasatful well, hosting videos is expensive. google/youtube is not going to do that for free. you can always find a subscription based service with no ads and pay to not see them.

[@inphynity4296]

2:24 My reaction to this vid

[@PLBXNews]

Same man :0

[@suns_out_7610]

:0

[@kithkin01]

I'm so fucked. I don't even understand this stuff and it's day 2 of college algebra.

[@kithkin01]

ImVenting you're screwed. Withdraw

[@TooooooooooNify]

stefan adams lmfaooo na, i somewhat get it after watching it 3 times.. its a summer class on top of that so the pace is overwhelming -.- time for me to find another video on another topic for this test.. how did you on your test tho????

[@kithkin01]

ImVenting I freaked out and got a 77... I was locked in a class box and they wouldn't let me pee :( I talked to the college and got Trans to an easier course... I'm retarded

[@kithkin01]

william ortez I'm happy for you. I moved out from my drug addicted parents home in 8th grade. I kinda missed some things

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[@janisayrahernandez8836]

You are seriously so amazing. My teacher can't teach and omg I understand it now. Thanks!

[@commanio]

from morocco, i want to say thank u man thats very helpful tnx again

[@Syruscleat]

Even though my mind is involved in Calculus 3, anticipating the study of Partial Differential Equations, it's good to get refreshers in the basics so to not forget where I came from. Thanks a million Pat! Or should I say in Math Talk, thanks infinity Pat?

[@KingCornWallis]

Yes! Great refresher! Also, I love the brief summary at the very beginning of your videos. I hate having to watch an entire video for one small note in the middle.

[@armeniarule]

Man your videos are so good, that my calc teacher tells us to watch them. Thank you very much.

[@dantaz]

Thank You do much patrickJMT , my teachers dont teach as well as You, and this small videos make me understand instead of memorizing, thank You man

[@memeauhme]

I have final exam today!! and I'm very lucky that I found your videos. Thank you!!! :D

[@ihlove22]

I've been searching for help on domain all week thanks you so much for making this video!

[@x0jasmin]

thanks this is sooo helpful, i was completely lost in class when we went over this. your videos are lifesavers:))

[@TarheelProduction]

WOW! I usually don't comment on videos, but this video changed my life, thank you so much.

[@analenaruffolo8691]

ur videos have been saving my life since 2016

[@patrickjmt]

time to be a supporter on Patreon! :)

[@TheEngineerVyoung]

Thank you so much for making these videos on Domain and Range. I'm about to go take my college Calculus 1 final and I always forget how to do this.

[@patrickjmt]

@staacyum well, you can have negative numbers under odd powered roots

[@kateholden9978]

Got my GCSE maths in 3 hours, this helped so much!!!

[@enjoyablesounds]

Great video...I have a feeling, as time goes on, my list of questions, uncertainties will grow larger and my frustration only deeper, therefore I seek help. My first point is domain notation. For instance the following -1 < r < 1 Here "r" can sit in between -1 and 1, where these two number are not included, if I'm not mistaken. However if you would read this from left to right (usually the way the majority of people read sentences) you would read " -1 is smaller than r and r is smaller then 1"

[@AYMENSHAHID]

"you watched this far go ahead and suscribe" i thought fair enough and i suscribed , thx for this vid, really helped

[@patrickjmt]

@RaeGlvr thanks, glad u like it

[@iMishYooh]

I was mesmerized by your perfect handwriting. Great video too. refreshed me for math150

[@vikasdhand2536]

So far the best mathematics professor 🙏

[@AshleyLowis]

So you're seriously AWESOME! This really helped me! I have a huge math test tomorrow, and this made me understand thing a little better! :D

[@soodmm13]

you are awesome man! i take calc and its the little stuff i forget how to do. so its super nice that you have compliments for complex stuff. I will be sure to reccomend you to my peers!

[@caprix1540]

Bless you. Test tomorrow and now i understand. The number lines helped so much. Thank you!

[@nicoargca]

Man you explain soooo well, I was wondering if you could give my teacher some lessons on practical teaching techniques lol

[@kevinmasterflexington1839]

thanks for all your help. your the best math teacher on the internet so thank you very much

[@EggoMcFrenchie]

Your videos are saving my grade in Pre Calc. My teacher isn't very good. Thanks!

[@patrickjmt]

the range of the f(x) is the domain of the inverse function. so find the range of the original

[@jeepersitsmeepers]

22 people can't find the domain and range... from a graph or functions.. thanks for the help on my final in pre-calc and giving me a reason to be on youtube and I CAN call it studying :3

[@davemayer6128]

your far beyond what my teacher would taught me thank you

[@meeheee1139]

This literally gave me some ideas that I never thought would be possible. Nice vid

[@Thebkdhomie]

Dude..... You prolly just mad my grade go up. cant thank you enough man

[@patrickjmt]

@staacyum well, you have to ask yourself: what restrictions are there for a cube root? can i cube root any number? (yes, you can). so here the only problem would be having zero, since it would be in the denominator.

[@patrickjmt]

@TheNorthfaceskater well it just depends on where the absolute value is and what the function is

[@24ctuoleg]

Thank you for all these videos. I don't know what I would do without them

[@The0nionKnight]

Your videos really helped me out. Thanks for taking the time to put these together!

[@bestsinger1289]

O my goodness.. i have always had a problem understanding this topic... I get it now...thanx to you...thank you!!! thank you!!! thank you!!!

[@GuardianDiancie]

My pre-algebra book gives less details on how to solve functions (and I mean its confusing.) So I had no choice but to see if you could help and you did. The book shows examples of Quadratic, Cubic, Absolute, Square Root and Reciprocal Function, but the point is that after they shows the examples, they don't make you practice a question like it, they scrambled it up like under the example for Reciprocal Function you will see an Absolute Function problem.

[@ayehoto]

thanks man you taught me more in 11 min than my professor taught me so far this semester

[@telemyumad4645]

what

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You're a disabled dunce

[@Hello_am_Mr_Jello]

Are you still watching ....

[@patrickjmt]

my pleasure, good luck on the test!

[@patrickjmt]

@darkhorse1723 well, then there are no radicals and no fractions, so there is nothing to worry about; ie, the domain is all real numbers

[@kcdc]

Thank you. You just helped an aspiring Computer Science major!

[@jailow1]

Mr. Patrick i loved the way u explain maths n i wish to see u in a video with a complete pic of u i mean i can u do make a video on a board so that we can see who is the tutor Patrick ... thanx

[@patrickjmt]

@mike3177 thanks for letting me know! i am trying to make sure there are no ads in the middle of any of the videos!

[@dorki3]

you are saving my college career. Bless your heart.

[@toastertomattoe]

you sir are a champ for precal students everywhere

[@jquikshot]

@marwen05 he is looking for the value of x to exclude in the domain that makes the function undefined (can't divide by 0) which he extracts from the interval (-infinity,infinity) by splitting it up and putting a parenthesis next to 2 which means do not include in the interval.

[@Zadamss]

These videos of yours are extremely helpful. Thank you.

[@moonshiry]

still the best tutor on youtube

[@ii2Proii]

Dude this guy is a BOSS!!! way better explained then my teacher@ i love you bro your great!

[@patrickjmt]

@TheDarkSaint777 my pleasure ; )

[@valeriatorres9634]

Thank you! This will be in my exam tomorrow and you just saved me!

[@AlesheaDominique]

Dude, this video helped so much. Let's hope I can now do this on the test!

[@XOSiren18XO]

Thanks for helping. Math is never my strong point. I questioned why I took Functions when I'm not very good at it. I guess it's because I wanted to learn as much as I can from the major subjects.

[@thegrandmaster1829]

Thanks a lot, cleared my confusion

[@itsMangostine]

this video is going to help me on my calc quiz tomorrow thanks patrickJMT

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you have just saved me from a test tomorrow morning thank you so much! :D

[@asife90]

guys the video was about *finding the domain* it wasnt about *writing U in the right place* atleast appreciate what hes doing for us...

[@Ichi-Bunz]

gonna get that A+ in pre calculus test tomorrow. Thanks for the Help!!!!

[@patrickjmt]

thanks, glad you like them :)

[@peacelovejonas094]

thank you so much! i actually get this now! you teach me better than my teacher/! im gonna be watching your videos a lot now!

[@6Diaa9]

the infinity part use to make me go crazy! now its clear :) thanks to u!

[@patrickjmt]

@ThaStonerDave yes, the very, very deep mysteries of 8th grade algebra

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Thanks for publishing these kind of videos! this one was helpful for me! thank you very much!

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Very helpful, I'm hoping to major in History of Mathematics when I go to college in a couple years.

[@NovaEX1]

I laughed so much at the D: drawn at 4:37 Took me some time to comprehend why you drew a "sad face" haha (: Keep up the good job!

[@KrisYeolExo]

thank you so much!! you are saving my life and many other students! love ya xoxo