Graphing Piecewise Functions - Precalculus

This precalculus video tutorial provides a basic introduction on graphing piecewise functions. It contains linear functions, quadratic functions, radical functions, and rational functions. This video contains plenty examples and practice problems on how to graph piecewise functions.
Domain and Range - Free Formula Sheet:
bit.ly/4eheN2W
___________________________________
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 and Range - Free Formula Sheet: bit.ly/4eheN2W Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Functions and Graphs: kzbin.info/www/bejne/kIWop2uFo6yUrtE Transformations of Functions: kzbin.info/www/bejne/qqq0faNsrZJ6pbc Graphing Polynomial Functions: kzbin.info/www/bejne/qICylpmaprKpqqM

[@lucasisasi9759]

3:16 why he choose number (y: 5),somebody can help me please

[@hbrymiri8301]

@@lucasisasi9759 he added 2 to x because 3 is greater than 2 we replace x with 2 giving us 5 in total.

[@Nickson-Mpinganjira]

❤❤❤ keep up the good work🎉

[@kenphiri5876]

wow he's my most favourite tutor ever though his identity does show up

[@CarlosCooksChi]

His voice always calms me down during my pre-rest panic attack

[@Sade_gl]

LITERALLY

[@charlottesphie7037]

HAHAHAHA. YOURE CORRECT

[@slugsarecrunchy]

After 2 weeks of struggling with this, I am watching this the night before my test...and in just 11 minutes, everything made sense to me

[@deffokay5879]

2 weeks?? Bro my freaking teacher got through this in 4 days. Day 1 is learning it. Day 2 is a worksheet. Day 3 is review for test (on your own) and day 4 is test. This is so unfair

[@slugsarecrunchy]

@@deffokay5879 well, we had multiple lessons on limits. I was basically behind on everything and my calc teacher loves to ramble on and on and get all theoretical, and my level of conscientiousness in extremely low 😖, that's why. Thankfully he's teaching it much better now. It all makes sense during class 🙂

[@CourseIsaacDoesIt]

@@deffokay5879 my teacher gives the homework, then explains the lesson the next day, then test the next. She is probably the worst teacher I’ve ever had but this video is the most helpful thing ever

[@perrycrotty7624]

@@deffokay5879 bro we had half a 50 minute period on it i am so fucked

[@heyitskara3292]

Ha I wish mine was this way. We just learnt this a day ago and she’s already putting a test on it in front of us. She does this everytime we learn something. One day to learn it, one day to study, and then a test on something we barely understand.

[@Highlife904]

i literally never talk in class and i pay attention but i still dont understand lmaoo

[@cesarnavarro6915]

Matthew Field yooo same lmfaooo

[@amberh7171]

Same, and I have a test on it tomorrow and literally no one in my class gets it

[@tennellcolbert8859]

Matthew Field same

[@connor12912]

this shit makes zero sense

[@victorlikescosmicbrownies]

Same this is the one thing I don't understand

[@jimmys7705]

I feel like 90% of the math I learn, I will never use other than to show people I failed at it

[@imgonnasneezeachoo]

I have a friend studying aerospace engineering and she's studying certain physics and calculus she knows she's never going to use. Its everywhere man Like hell i wanna be a nurse,other than half lives, when am I gonna use quadratics lol

[@nnnn50001]

+ - • / is all the math you’ll need

[@user-oo5xy3ee8o]

right i feel like all we really need to learn is the stuff in elementary. Addition, Subtraction, Multiplication, Division. But after that i feel like people just got bored and said “Well we have to teach them something lol” and just threw some stuff in there. The stuff they have us learn isn’t able to be used. You’re not gonna put on your resume “I can do piecewise functions 😀” after elementary, you should have some time to figure out what you want to be when you grow up, and dabble in a few things. Then you should go to school for the thing you want to be. Like if you wanna be an accountant, then you’d go to school for that, a doctor, a painter, a photographer, etc. and learn the stuff you need for THAT thing. _okay that’s the end of my Ted Talk thank you_

[@jimmys7705]

@@user-oo5xy3ee8o posted this 10 months ago and I still dont know how the fuck to do it

[@natnaelgirma2071]

True dat

[@abicados2386]

i feel like im getting it at the same time not

[@dionel1388]

Oof

[@abicados2386]

One year later and I still don’t really get it :DD

[@icesnowflake5510]

@@abicados2386 lmao, I never got this eithet

[@frankg2579]

tmr test, plz pray for me....organic chemistry tutor my last hope....

[@dionel1388]

@@frankg2579 Good luck and God bless! You can do it! 🧡

[@2b2c1d2]

For the people who are still lost, what he is trying to do is combine the functions with the given parameters/limiters, whatever you want to call it. He is taking part of a function and graphing it on the same graph with each rule, and the first example itself explains it very well. Basically he graphs both graphs, but uses the x value limiters (x>/=0 and x

[@manveersingh9490]

noob

[@tayluvofficial]

Nah got nothing and imma fail 😭

[@CHILDPROTECTIVESERVICES]

What are you yapping abt??

[@charlottesphie7037]

Bro you make it even worst. This is very hard. 😅😅😅

[@emmanuelmanuel4824]

You’re the best tutor on KZbin God bless you and keep up the good work

[@bobbrock4221]

I really like the Khan Academy as well. To be honest I think TOCT does a better job of really breaking it down into a way that I can understand. Except for this section, I'm not grasping it

[@carreeeck4384]

Agreed

[@chernobyl6758]

That moment when you understand it just fine but still can't do it for some reason...

[@idenafshar3451]

Me right now

[@daftspect]

literally!!! it's so annoying. like i get it in class but when i do seatworks im so lost

[@autumn5108]

me rn

[@rafaellamalca5629]

RIGHT!

[@samiraabdelhady92]

pov: you have a test in 2 hours and you're just now studying for it

[@masonharvey6149]

I’m in a study hall without headphones rn so I’m studying with subtitles

[@donthaveausernameonmind7450]

@@masonharvey6149 not same externally but same internally if that makes sense ,Iam also using the subtitles

[@emmagraceberardelli5057]

Yup

[@emilymurphy1084]

the night before but yes

[@j0ker_Editor_Channel]

ME RN

[@saraimejia123]

tutor: take your time graphing step by step and you should be fine. It's not that difficult me: still gets it wrong

[@CarlosCooksChi]

sarai mejia lmao

[@roshrosh8991]

Relate🤣🤣

[@LordOfTheUnderworld]

THANKYOU. MY TEACHER WASNT EXPLAINING IT AT ALL. YOURE A LIFESAVER

[@PotatoPhoneUser]

That's it. I'm failing math and I'm a piece of disappointing trash.

[@alilnobody5672]

Goodluck haha

[@anthonyw6895]

Sir Sykes don’t give up, keep going

[@darkside-tr2gj]

no ur not lol, literally everyone is bad at math. my mom, who is a pharmacist, is bad at math. you will get it eventually. its easy but has many factors

[@sageofintellect6437]

I used to say that i was bad at math. I used to fail tests like a champ and offer petty excuses. Until one year I made a commitment to myself that i would try to get an A. It was hard and the grading policies were tough but I realized that the only reason why i was bad at math was because I simply did not care at all about the class. I was lazy and did not want to try. I always believed i could not do good and that was the problem. I didn't pay attention in class or even care to listen to the teacher so I was constantly confused about the homework. It didn't help that i had not been paying proper attention in math for the past couple years as well. When i finally realized that this was the reason why i was bad at math and i began to understand how school worked then my test scores skyrocketed. Of course having a good teacher and you tube videos like this helped a lot but i was the one who was paying attention in class and doing the HW. I ended up with a B overall in the class and was very close to an A. So never say that you are bad at math or that you are garbage because i can assure you that you aren't. You simply need to get in the mindset to succeed and then work your butt off. You will face many difficulties as you try to improve in math but these difficulties will teach you many things and give you the skills that you need to succeed in other subjects . trust me. All you need to do is put forth the effort, start paying attention, and stop making excuses/being lazy. this was my experience. I hope you learned something.

[@youngstarsgrinding]

Bro this school stuff doesn’t define you. You don’t need to get good grades to be successful. Keep ya grinding and keep ya head up

[@Jay-pc2ev]

I'm still lost lol

[@filobatirsarkis646]

do you know the way

[@eymme5571]

Lol same

[@monkeyman2432]

Here

[@lexiesmiski]

Same wth

[@windygraphics6131]

he explains pretty bad its easier than that

[@JohnArrowShorts]

For the people who are still confused after this video. I suggest watching other (youtube channel)videos related to this topic. Based on my experience i watch 10 youtube vids (different youtubers) in order to grasp the concept and every youtuber explain their idea about the concept of piecewise function graphing. For me after watching different vids. I come to conclusion that there is different ways to graph this piecewise function and our tutor in this channel use different method in every problem (thats the confusion comes)but if you can find a comfortable way to graph, stick to it.

[@eymme5571]

Ok, imma do it

[@revoltanimation8957]

thank u broskie

[@anonymous-nu9vs]

Basically.. you'll need to know graphs of different functions, inequalities and set theory and

[@Lou_Mals_San]

ahhhckk thank u for ur comment, that's whyyyyy

[@emilymarines2545]

me crying cause i still don’t know how to graph piecewise functions

[@LXVIII-21T]

hi Emily

[@charlottesphie7037]

Hahahaha youre not alone

[@MsHortel]

Professor's voice calms me down and opens my brain to understand. The best therapy ever for my math trauma experience.😂😂😂❤

[@seamusmoran4776]

I cannot thank you enough for these incredible tutorials I just started pre calc and you are a life saver

[@surgere1980]

taking math classes online that barely give detailed help or explanation and the teachers almost always on break is recipe for disaster...until organic chemistry tutor videos exists you fr carried me in my online chem and pre calc classes thank you :)

[@HBLK702]

there is no peace in piecewise functions

[@blankb.2277]

Love this! Great intro. Guys if your still confused, just do a ton of practice problems and have Photomath show you how to get the answers when you’re stuck.

[@mohammadaljarwan719]

It’s complicated f*s💔

[@thegamer5439]

My teacher could’ve just played this video LMAO

[@nabihah2674]

then your teacher isn't doing their job

[@theiv_aj]

litteraly

[@AzongLee85]

wow this is so helpful, much more than my college preCal's textbook. Textbooks are written professionally and they don't include tips or easy-to-follow steps, but you make learning math really interesting! thanks so much and i'm also looking forward to purchasing some of your merchandises!

[@dngrtegaijin4680]

I watched only a min of this video and got it right away. MANY THANKS!!

[@Elpepe_0245]

Why do I have to know this!

[@newsterkun1336]

Best question

[@sageofintellect6437]

@StevenMora you don't It just teaches you the type of critical thinking you need to learn actual math that you do need to know

[@j.s.2958]

@@sageofintellect6437 I learned that kind of critical thinking a million times before in middle school. I don't need to learn how to do critical thinking over and over and over and over again.

[@DanaLea57]

@@j.s.2958 Yes you do.

[@marvin-cw4tw]

@@DanaLea57 no da fuk u dont, this is a pointless waste of time

[@laurenorourke2442]

piecewise functions are the death of me😭😭 i asked my teacher for help after class today and he was like range is very difficult to find💀💀 so i had my twin brother who’s in calculus to help me. But this video helped me understand even more so thank you!

[@mohamedalzedawi141]

gave you the 69th like, congrats😃

[@namiip]

Finally! I’ve been struggling with this since our school uses Aleks, but it doesn’t explain this well enough.

[@eseluh]

literally the best channel

[@jianzhonghuang164]

This videos makes sense for me, i even can understand what he said, incredible.

[@c_f_op6366]

idk what id do without these videos

[@creatorcuber]

A math tutorial with a clear voiceover!

[@dannyjesse1149]

Can you please give reasons as to why you take certain steps? Like why you picked the the positive side for when y=5

[@Hakirasha]

THANK YOU SO MUCH WITHIN 1:47 YOU TAUGHT ME MORE THAN MY TEACHER

[@winkwonk9787]

My homework is like this but 10x more complicated

[@justingenilo6522]

Good luck to everyone in finals!!!!

[@dionel1388]

Thanks! :)

[@bilahhakim]

wait why -2 squared is -4??? Its actually positive right????

[@xmascarol3962]

bilah These two are different -(2)^2 and (-2)^2 since it didn’t include a parenthesis im pretty sure he assumed it was -(2)^2

[@isabellawilson3948]

XmasCarol true that

[@coolaverage2017]

He correct

[@jacobrye3949]

-2 squared is 4 not -4

[@ehhhhh596]

Wait where did that -2 come from???? Pls help me

[@MyHam-os4bq]

“Graph it step-by-step, it’s not that difficult.” Me, repeating PreCalc 1 and feeling attacked: 🥴 lmao

[@NicoleMargaretPCena]

Youve been my savior for yrs but for the first time im lost 😭

[@NOODLEKONG17]

I have an exam in 2 hours and I'm just learning this now

[@LeianCharlesRamas]

Literally watched this for 2 hours straight, I finally get it lads🎉

[@neycrisleo10730]

Man this guy's a Multi talented he knows every single subject 🔥

[@aniganjian4619]

This was so helpful, I learned this months ago but this was the perfect way to refresh my memory.

[@DeeJayFuego]

Im confused at 3:20 when you say "its going to be at 5" how did you get that?

[@Saltiiboiiiyaknow]

I’m pretty confused about that too. I assume he added the 3 and 2 together. So maybe 2=y

[@MichaelScott934]

Thank you so much I've learn weeks worth of work in 12 min

[@followhrcdraculadnan2650]

This helped me a lot on todays pre-calc quiz, I missed the first lecture and missed out on this, but thanks to your video I was able to understand the concept and solve the problems in my quiz. I am genuinely grateful. Thank you very much.

[@RuthM1611]

you doin this in pre calc! 😭Why I have to do this in Algebra 1

[@CardboardCow]

It all makes sense now even after 1:30 in I was gone when my teacher was teaching this so I needed to see this❤

[@codex7299]

One again Thank you very much. Math is a practical thing to me ,like cooking ,you really help simplify the 2 page notes they give us in class, and just simply show us "which is what" and what is being requested❤😊

[@HYPERDYNAMYX]

i came last semester to understand piecwise and could not, and failed the test, but now, when my end of year exam is tmmrw, i finally understood it!

[@omarabouzeenni6754]

how is a guy on youtube teaching better than my 9th grade math teacher

[@MyinaMacy]

Thank you I’m in an accelerated class we go over the concept once and test at the end of the week. Big help. 🙌😌

[@aimanfariz7642]

At 4:39 you plugged in 1 in x, but it is stated there x is less than 1. Can you please explain? I'm confused right now.

[@moosypoomoza1020]

Facts i dont get it💀

[@Artemismission2025]

You can plug in any x values just for locating any points. What he did is like a bypass which is acceptable there's no wrong with it, he set the value X at 1 for easier execution.

[@alilnobody5672]

you're an amazing tutor btw! You made math a little easier for me... Just hope our teacher will too >~

[@averygattis143]

You have saved me from a great deal of pain , thank you sir

[@apejit7205]

I dont get it👳

[@roseashley8602]

Ok piecewise functions are functions that consist of multiple functions on a graph and you will be given an inequality and you graph or subtitute

[@elleloveayou]

Thank you po, tomorrow we have a quiz and hopefully I'll remember what I've learn from your discussion❤

[@S-be6gz]

Whoever sees this, God bless you and have a great day

[@tambahsaah8005]

Your lecture feels like your re walking along with me in my brains!!! Thank you so so so so much😢

[@Chef_Ramsay]

You need to compare all the math equations he did so you can understand how he did it. That’s how I somehow managed to understand his lesson.

[@michaela4479]

srsly, thank you i might be able to answer smth at our test tomorrow

[@bryanescobar8235]

wait in 6:30, -2^2 is 4 right? not -4..?

[@georgesadler7830]

MR. organic Chemistry Tutor, thank you for Graphing Piecewise Functions. These functions are linear, quadratic, rational, radical and constants. The TI-83/84 Calculator is also helpful for Graphing Piecewise Functions.

[@emilymurphy1084]

how is it that you explain it so much better than my dc college algebra teacher ever does.

[@aeshashha69]

thank you so much i literally had no clue what was happening in class, and you just helped me so much because i have a quiz tm

[@LaeteteaEngelbrecht]

Watching this 2 hours before my test and hopefully I'll do good 👍

[@overusedpenoutofink]

I understand it better now! You’re a life saver TwT

[@m3owmaster]

this just saved my booty, thanks man you the best

[@typicalmountainbiker]

I'm so surprised that I understood any of this. Thank a lot!

[@JackieDaytona2749]

At 9:11, i have no idea where you got (4, 2)......... Where did that come from... You said the square root of 4 was 2 but where did you get the 4 to plug in for x to even come up with the square root of 2... I thought i was finally getting it and then you just said that without explaining where you got it from. Where did the 4 come from?

[@johnmarkfayo1573]

Its automatic because x is greater than 1 which is we cannot go at less than 1 but we can go further more to infinity at right (he meant just to where the graph will go that is why he input √4 because √4=2 which is (4,2) in the graph √1=1 is (1,1) then √2=1.4..is (2,1.4) √3=1 (3,1.7) √4=2 which is (4,2) tips you gotta understand how each math models graph)

[@francisuwalaka8370]

Tnx so much Understanding this has never been easy

[@Jshao.xd.]

I’m still confused, I don’t even need this in a regular job 😔👊

[@muhammadmahad3002]

I didn't know this was pre calc, I'm taking this for my algebra 1 class.

[@robbysrad7519]

me too and my brain doesnt like this at all

[@shammahchilonga7995]

Thank you very much mr.... I've really been helped..🙏🙏

[@jackyu8825]

Thanks. This video really helped me learning Algebra 2.

[@yashpatel2345]

I saved me dude ur the god

[@jjonnto]

idk but this is kinda the same but much better to understand For example: f(x) = {-3, if x

[@alanbeckerson8482]

Me at 0:00: I'm ready to learn!! Me at 11:58: whaaaa????

[@rolandfrancisco5591]

BRO, YOU ARE A LEGEND, KEEP UP :)))

[@newlinnn8194]

This video was more helpful than my teacher

[@venghettomusic2959]

organic tutor is a king mh

[@legendarybeams6487]

You are a bloody legend

[@ParisShenae]

Thank you from the bottom of my soul for this fast video!!!! Geesh

[@joyshaba713]

0:35 I don't understand. How is it a diagonal line?

[@ameykadam5195]

If the eqn of graph is linear ( with degree 1 ) just assume the graph would be a straight line

[@mr.komane9073]

Wow, thanks a lot bro u made things easier with that hyperbola example in between. Daya dankie ones again and keep up the good work hey

[@michelle_digitaldiaries]

This guy explained it better than my teacher

[@jeonkasey7517]

helped me a lot especially under isolation

[@ninacilliers3225]

what would I have done without youtube

[@Ilvzxo]

Watching this 10 minutes before test…

[@aqbkq]

Night before exam lol I don't know even math have this

[@brooksdavis9150]

You need to explain this better, why does it have a y intercept of 3 and why does it start at 5? Please explain!

[@kurtishacharlery]

Yur videos areso helpful to somone like me who's just starting calculas 101

[@fanwee5048]

Kurtisha Charlery this is alg. 2 dipdick

[@l0lgirl675]

u wish it comes back to haunt u in pre calc

[@kurtishacharlery]

@@fanwee5048 didn't say it wasn't . Just saying that this is the one of the first things you do in calculas 101 n this a helpful video. Smh

[@kurtishacharlery]

@@l0lgirl675 yep😭

[@lolzxl9184]

Dafuq what do you mean, I’m doing this in 7th grade

[@biillyguote532]

5:45 i am confused.. Isnt -2squared suppose to be +4?? Yk bcuz a negative x negative is a positive¿ please get back to me on this....

[@SM-qn7sr]

You’re not squaring -2 * -2. Youre squaring something positive: 2 * 2. The negative only applies after you square it

[@Pro_Beans]

@@SM-qn7srsquaring a negative always makes is positive. Bc you multiplying the number by itself.

[@SM-qn7sr]

@@Pro_Beans there’s a difference between (-2)^2 and -(2)^2

[@NightcoreSkies]

how tf does a 11 minute video already explains better than my teacher does in 1:30 hours?

[@pbj7920]

I have math final tomorrow wish me luck

[@CBT-CucuyBirdTarado]

Imagine the teacher actually teaches the subject instead of reffering you to a video couldn't imagine D:

[@knelson1912]

Hello! At 4:15, why did you plug in 1 randomly? I am confused on that part.

[@ayrus890]

cause the end point says x

[@adamoja4295]

Don’t know where to put it . I really appreciate your playlists . If you’d drop a linear algebra ting would be gass .

[@jellyshark9695]

At 3:03, how do you know it has a slope of 1?

[@KeniaSalmeron-lr7wm]

Same I’m wondering the same 😂 now

[@omniballs9586]

The equation was in Y= mx+b m is the slope So x+1 has a slope of 1

[@cstrand]

in the equation x+3, x is the variable and the variable will always mean 1 unless there’s a number in front of it. so x would be 1 but 3x would be 3.

[@mahimsterunicorn7948]

KZbin videos teach me betters than my teachers/math tutors XD

[@elanorgreenleaf2274]

Using this for my pre-calc course and I like his voice, he reminds me so much of Mark Walberg talking. Same accent maybe? But its a good tutorial, Thanks!

[@why9774]

For a few seconds I didn't understood but after a couple of trial and error I did(guys you can do it, don't be discourage)