Graphing Piecewise Functions, Domain & Range - Limits, Continuity, & Absolute Value ,

This math video tutorial focuses on graphing piecewise functions as well determining points of discontinuity, limits, domain and range.
Domain and Range - Free Formula Sheet: bit.ly/4eheN2W
Limits - Free Formula Sheet:
bit.ly/3T3dD2X
__________________________________
Introduction to Functions:
• Functions - Vertical L...
Evaluating Functions:
• Evaluating Functions -...
Function Operations:
• Function Operations
Increasing and Decreasing Functions:
• Increasing and Decreas...
Relative Maximum & Minimum Values:
• Identifying The Relati...
_____________________________________
Relations and Functions:
• Relations and Function...
Domain and Range From a Graph:
• Domain and Range of a ...
How To Find The Domain of a Function:
• How To Find The Domain...
Average Rate of Change of a Function:
• Average Rate of Change...
The Difference Quotient of a Function:
• Difference Quotient
_____________________________________
Evaluating Piecewise Functions:
• Evaluating Piecewise F...
Graphing Piecewise Functions:
• Graphing Piecewise Fun...
Composite Functions:
• Composite Functions
How To Evaluate Composite Functions:
• How To Evaluate Compos...
Composite Functions - Data Table:
• How To Evaluate Compos...
Comp. of 3 Functions - Data Table:
• Composition of Three F...
Decomposing Functions:
• Decomposing Functions ...
_________________________________
Introduction to Inverse Functions:
• Introduction to Invers...
How To Find The Inverse of a Function:
• How To Find The Invers...
Verifying Inverse Functions:
• Verifying Inverse Func...
Horizontal Line Test - 1 to 1 Functions:
• Horizontal Line Test a...
Vertical Line Test:
• Vertical Line Test
Graphing Inverse Functions:
• Graphing Inverse Funct...
Composite and Inverse Functions:
• Composite Functions an...
__________________________________
Even and Odd Functions:
• Even, Odd, or Neither ...
Transformations of Functions:
• Transformations of Fun...
Linear Functions:
• Linear Functions
Functions and Graphs - Problems:
• Functions and Graphs |...
Functions - Test Review:
• Functions
______________________________________
Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections

[@TheOrganicChemistryTutor]

Domain & Range - Free Formula Sheet: bit.ly/4eheN2W Limits - Free Formula Sheet: bit.ly/3T3dD2X Final Exams and Video Playlists: www.video-tutor.net/

[@LeithB]

You are carrying me through college-level algebra. Thank you very much

[@tzuyu8788]

this is college level?? im learning this shit in 11th grade

[@LeithB]

@@tzuyu8788 Well I was doing this while in dual credit in the 11th grade, so meh. Last semester i was an 11th grader.

[@zfox5004]

I'm doing this in grade 9

[@priscillaz4108]

@@tzuyu8788 its reoccurring topic, I first learned it in 7th grade when taking alg 1 then alg 2 in 9th and now I’m in 10th doing college precalc and reviewing it

[@kaleblee1167]

@@tzuyu8788 IM IN 8TH

[@xClicKx]

Instead of reviewing my notes, im watching every video for every section im gonna be tested on lol. Your explanation is so easy to understand.

[@zunairahislam390]

THE FACT THAT THIS MAN MADE A VIDEO 7 YEARS AGO N IS HELPING ME IN 8TH GRADE RN TYSM

[@miahayes8985]

I used this video when I was in 8th grade too and now I'm using it again when I'm a junior in college so it's crazy how he has helped so many people throughout time and continues to!

[@WorkinehAmanuGashu]

Absolutely

[@Bkboy911]

2 weeks of learning done in 30 minutes, sweet.

[@originalgrandslam]

My 8th grade algebra teacher was teaching this and I have mid terms coming up so I had to review this topic because it confused me so much, so far this is helping a bunch.

[@yabaz800]

yo what I know now you are at your 9th grade but how come you studying this at year 8, anyway gg

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bruh your school's lesson is so adv, where's that??

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If I was a millionaire, I'd hire you as my private tutor.

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[@brendenlang9593]

Bruh literally first 4 min did better than a weeks worth of my teachers teaching

[@lioraisrael7231]

Your video really helped me get through this lesson. I believe it had something to do with the way that you broke up the solution process. Thank you so much.

[@Frost-em1vb]

Your explanation was great and helped me significantly. Thank you.

[@abdullahe3674]

truly wonderful, i can imagine how much effort it take to make these videos . thank you :)

[@seonhuidu1501]

hi, for the domain of the third graph, shouldn't it be 4 instead of -4?

[@별도혁]

나도 이게 이해가 안되네

[@noboniahasan8213]

I have the same question😐

[@itsmebymyself8033]

It should be D (- infinity,4) U (4, infinity)

[@MoherZO]

I had same problem

[@Malakititi2025]

Yes it is +4

[@dishsoap5317]

you are such a g i think imma pass my exam bc of you!!

[@sabrina.pianist]

You make my professor look bad, I’m actually learning and I haven’t recalled a moment in life where I actually learned since I took geometry in my sophomore year of highschool so thank you

[@uznaimat7072]

Thank you. This is going to help me so much for my math college courses. Thanks a bunch.

[@YoungVinny]

23:10 hmm should be +4 not -4

[@famfam7266]

Oh thnak you thought i was wrong

[@shaziedalam4074]

Yes

[@thedajamari3828]

Yooo, I was thinking the same thing

[@emmanuelrodriguez7022]

taking calc over the summer so trying to get a head start thank you for your videos :D

[@theunseen6935]

the domain for the last example is from negative infinity to 4 and from 4 to positive infinity. you said it was up to -4 which is wrong

[@therickestpicklerick]

Glad you learned!

[@kathy2766]

Bro tysm I’m literally failing precalc rn and I need to pass my exam tmrw and I finally understand

[@vordivask4059]

Really helpful and figured out exactly what I needed to know, thanks!

[@BEXIVLOGS]

At 23:10 shouldn't the domain be (-infinity,4)union(4,infinity)instead of -4?

[@sleepyhead785]

i think so should be +4

[@sawakokuronuma8689]

i was bout to comment that...

[@DK_75]

It should be +4

[@RahulRathi_Multimedia]

yeah I stopped at 23:10 to read comments. I knew someone intelligent would comment :)

[@abbasuddintasin5244]

How about this if I say Domain =(-infinity,-1)u[-1,4)u(4,infinitey) Is that right or wrong?

[@justinekoip9676]

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[@jadenc8164]

this guy is so calming

[@rubystars1919]

why can't I understand this WTF

[@imdonelol4495]

Same. 😔🤜🤛

[@fphrogz7261]

omg Kageyama LMAODKD but SAME OML

[@luigiman64]

Well I'm dead

[@alphakennybody70]

Yo bro this is hard asf my nigga

[@waynenayem1957]

Learn functions, finding domain and range, graphing functions first

[@simthandileqhunyana1798]

its 2022 and your videos are still useful

[@kotosqoposrly]

When I learned about Limits last week on college, I went full Cady Heron in my mind =]

[@mamoonamahmood2912]

Always appreciate a mean girls reference 😌

[@krkmjr8429]

u study this in college???

[@kotosqoposrly]

@@krkmjr8429 it was university to be exact.

[@nandolance91]

@@krkmjr8429 you have to know how to graph piecewise functions to evaluate limits in college

[@krkmjr8429]

@@nandolance91 yea im learning graph rn on high school

[@azizpatel4907]

you are a life saver...

[@Fortunate_crown]

Wooa! I just hit on it now! Do not bother. I just thought better of it. For the first case, y = - 3; so, it is not dependant on x. Hence, we are safe to say the range of values starts from - 3 since y is - 3.

[@stefanpetrovski5793]

OMG THIS VIDEO HAS EVERYTHING I NEEDED. THANK GOD I WILL PASS MY CALCULUS 1

[@btslover2.048]

calculus 1 I’m learning this in algebra 😭😭

[@erickreyes7547]

@@btslover2.048 same alg 2

[@nametsogoitseonemoatshe1633]

@23:52 WHY IS -3 included and not excluded?

[@kamwendomusonda]

The organic chemistry tutor saved my life🥲

[@TheMostHigh13]

At 23:00 there is a mistake. We're only human. Could you put something in the video description to correct that? Thanks.

[@kimutaikelvinboen9073]

At(- infinity,4)U(4,+infinity)

[@emilyzhou5541]

Thank you so much! This helped immensely :)

[@alfonsobusa9921]

For the last one, the range should be [-3,0] U [0,3) U (3,infinity)

[@kienfattyam6195]

there's nothing there between -3 and 0

[@enriquezmatheorainiellen.8155]

question, can't I directly answer [-3,3)U(3,+∞)?

[@raniahabbas85]

@@enriquezmatheorainiellen.8155 that’s what I thought so as well. I’m confused about the range in last question.

[@purrpcaine211]

My question refers to the 2nd problem. Now im fully aware that you can't have a negative under a radical but hypothethically speaking what it you had a function of -x under a radical for x less than 0, how would you solve that?

[@nuggetx4086]

It isn't possible unless you use complex numbers

[@mrmathcambodia2451]

ok , I like this solution in this video .

[@luluangas5290]

At 21:31 why did you plug in 6 if you can do 5? please enlighten me, thanks in advance :)

[@yabaz800]

champ you are the best

[@georgesadler7830]

MR. Organic Chemistry Tutor, thank you for another off the mathematical charts video on Graphing Piecewise Functions, Finding Domain ,Range ,Limits, Continuity and Absolute Value. There is a possible error on the range where you have [-3,-3], please check video.

[@neffinsanchez4049]

21:31 why did he plug in the 6 was just random or did he have something else done before hand. thank you in advance

[@eshkolali6078]

big respect

[@Fortunate_crown]

For the range of the last question, shouldn't it be : R(-3, - 3) U [0, 3) U (3, infinity)? Pls, respond to this; so I can get it clarified. Thank you very much! Love from 🇳🇬.

[@omnivack9198]

At 23:50 isn't the "-3" supposed to be in parentheses() rather than brackets [ ] because technically it doesn't include -3...??

[@farnazkhan9267]

Yes exactly

[@gabebaste2550]

If you look at the graphI -3 is still included because the domain goes to the left continuously

[@NineONI]

Gabe Baste But it’s in regards to range not domain, therefore shouldn’t it exclude the -3?

[@somethingonboard5364]

Is it true that if you take MJ it would be easier for you to memorize readings? dos it also apply to mathematical formulas?

[@4raeye]

bro thanks so much

[@dayakarejnavarzala6746]

I'm a little confused...Shouldn't the first problem's range include the discontinuity on the y-axis?

[@nubianchick3667]

Can I hire your brain for like every second that Im alive?

[@bhekidlamini51]

Thanks!

[@cryptowithdaxza]

tnx bro

[@kapundapanduhi7259]

THANKS ALOT BOSS!

[@rowanmutwanamba5127]

The guy is dangerous

[@nurazmina1237]

Hanani tngok ni , aku kt comment

[@hananiradif1995]

Ya sayaaaaaaaa

[@nurazmina1237]

Abg kt video tu beleter ape , tam pamham amkum

[@arinzeanthony7447]

Is it even possible to find the range of such piecewise functions without plotting graphs?

[@haelraph]

Can someone explain 4:01 ? Why did he start with y intercept? Why doesnt both ends go infinite and only one has the arrow?

[@dwiaustralia4920]

Do you have video about piecewise function for wind direction with angle please

[@FLICITY]

I just came to know that his name is Julio Gonzalez

[@mazharabbasbukhari7390]

oh god,thatswhy this topic was so tuff,i never attempted this part in exam.and still mind become mouf.

[@hayleywilliams7346]

thanks

[@BWG05]

23:00 domain would be from negative infinity to 4 union 4 to +inifinity right; not negative 4?

[@jeffreycao6745]

yea

[@cyabits1]

i am confused with the use of ( ) and [ ] or [ )

[@diggittydoodoo]

You use "(" when the inequality uses less/greater than, while you use "[" when the inequality uses less/greater than OR EQUAL TO. Examples: x < 2 = D(-∞, 2) x ≥ 3 = D[3, ∞) 3 < x ≤ 8 = D(3, 8] 2 ≤ x ≤ 6 = D[2, 6]

[@MzwandileHarmans]

What is the value of f(x) if the corresponding y-value is neither a hole nor a solid hole but just a line. Do you read off the graph ?

[@mappuhhstudioofficial]

I would say you would have a horizontal asymptote giving a domain of (-infinity, infinity) and the Range is [1], the limit as x approaches -infinity is -infinity, and as x approaches +infinity is infinity.

[@PHILLYMEDIC69]

thanks julio

[@juheongbae5219]

basic high school level !

[@zeinabebron4849]

The domain for the last piecewise function should be 4 instead of -4.

[@MoherZO]

Yes

[@kimutaikelvinboen9073]

In domain +4 is not included not -4 ,,point of correction

[@dereksavauge6613]

At 24 minutes you said that it doesn’t include -4 but I think you meant it doesn’t include positive 4

[@anthonyviana7913]

isnt the domain suppose to exclude 4 not negative 4??

[@heechul-elf-2696]

yeah i was wondering the same this

[@mazharabbasbukhari7390]

sir u r great

[@sitinurlisabtizwani2408]

hi.. can i ask one question?

[@haiter347]

as you can tell id rather be around loved ones and not associate with people i have no clue about. It was a mistake, a massive one to be frank

[@haiter347]

different values and different aqpproach to business and frankly life. this is the end to whomever is inside my business

[@haiter347]

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ik watever i say doesnt matter cuz im a 2d caricature and have been for a long time to many of u

[@PaisPokopi]

Are you an AI?! Cos you're so cool.❤

[@anthonyroberson5199]

I can do the math is anybody else getting confused on the graphing part

[@jaskaranshekhon9990]

Why do we need those red statements?

[@candicaswanapole8539]

shouldn't the x asix of radical function start from 4 because we cant take 1 as it is stated in question x>1 ( not equal to 1 )

[@c4ne]

tysm

[@ilyasnur8704]

o chem broski I love you

[@Buddhabebop]

if 1/x only allows negative numbers according to its instructions how is it its range includes negative infinity?

[@nilaysingh9252]

how do you know when to put an open or closed circle when graphing?

[@TheOrganicChemistryTutor]

let's say if x is equal to or greater than 2, a closed circle should be used. If x is simply greater than or less than 2 but not equal to 2, then an open circle should be used.

[@nilaysingh9252]

oh ok thanks man

[@krkmjr8429]

4 years :(

[@candicaswanapole8539]

iam talking about question 2

[@juliannakatelig-ang2793]

If doesn't have any equal sign means open circle?pls enlighten me

[@raniahabbas85]

Yes

[@toxicmaniax5719]

At 21:18 why would you plug in four when it not x is greater than or equal to four it just x is greater than four, wouldn't that mean that four is not included in domain, why not use five? I just realized that four is included, I was only thinking of 2x-5 as an individual function, 4 is included because of the second rule in the piece wise function my bad.

[@winglessbling1499]

same question

[@cherlielynvalino8708]

why was x-1 equal to 0 became 1/4 x?

[@krkmjr8429]

fr he should say every step so we can learn

[@Bahenyi]

F of 4 is equal to 6...is this correct?

[@lanaichild926]

No, it should have been 3. Using either the absolute value equation or the linear equation you get 3.

[@AmmarAlKhatib581]

@@lanaichild926 im confused because of this as well, how did he get 6??

[@Jenilyn_Pisces]

Number one thing is these videos don't explain how they get the answer they just know so they write it on the graph but never explain how they got it

[@AmmarAlKhatib581]

hello, how did he find f(4)=6 in the end?

[@baltimore21]

22:51 sec the domain will be R - {4} not -4

[@raisasultana2077]

In last example the domain is wrong. It is 4 not negative 4

[@Dappa-fv7zg]

good video but just not as long tho👍

[@naimatullahkhanitistruth5062]

Before to solve the question plz sir define the topic first.

[@DragonKidPlaysMC]

Naimatullah Khan it is truth he has other videos on this mate...

[@naimatullahkhanitistruth5062]

@@DragonKidPlaysMC send a link plz

[@jaimelynn6464]

THE LIMIT DOES NOT EXIST!

[@GamingWorldMoments]

its+4 not -4

[@kristinemarcelino6805]

can I ask for help?

[@raniahabbas85]

23:08 why is -4 in the domain?

[@kitcatangames9045]

Isn’t 3 not included

[@SheikhAlviraihan-fo5nc]

In 23:02 why did you take negative 4 in the interval of domain? Can somebody please clear this doubt?

[@hasanal-dhubaibi1507]

I guess that was a mistake, also I guess the range should be from [-3,3) union (3,+infinity) not [-3 to -3).

[@sseagle4173]

⁠@@hasanal-dhubaibi1507Why is -3 included tho? Asking because thete is an empty circle

[@muaazkhan5388]

i still dont get domain and range its so confusing

[@bolinozenonsantiago8968]

te amo

[@ashnabeechook2829]

x --> + infintity, means x aproaches infinity from the right !!!!! not from the left !!! this is completely wrong

[@frost.707]

What? no. It means x is approaching positive infinite.

[@hunterknutson2665]

bahahahah, no. how could a value approach positive infinity from the right? that would mean X is greater than infinity, i.e. not possible. Think about that for a second...

[@madmaxrex7563]

X approach + infinity means it approach from the left, and x approach - infinity means it approach from the right.