Graphing the Greatest Integer or Floor Function

[crossviewmusic101]

GO GCA!!!

[crossviewmusic101]

my math class sent me here;)

[iBall12]

with continuity, why is this function f(x)=[x] continuous from the right but discontinuous from the left??

[Acontador13]

Damm this question got me on my test! f(x)=Ixl+[-x]

[xcmiler181]

okay so what if the problem is [x-2] + 1?

[hippobunz]

what if its like y = [x + 3]? does the graph move to the left?

[patrickJMT]

@hippobunz probably! : )

[FDLMath]

@hippobunz yes, it moves it to the left by three units because the "3" impacts the x-value before the greatest integer function has a chance to work on the x.

[daivonisc00l]

yous a life saver! Online school doesn't explain very well be you're a real help.

[paulan25]

Thank you so much!!!

[graypaw300]

THANK YOU.  I've decided I've learned everything the best through youtube...

[Mel050991]

how about f(x) = [|x+2|] -2x squared?

i love how u teach coz it seems so easy...but my teacher is giving us difficult equation and i can't really find a way to do it..geez..lol can u upload a more diff. eq. with a solution? pleaaaase? hehe

thanks!

[lawrence431]

how do you graph this one

f(x) = [x] + [4-x]

[IkonPhenom]

Sorry about the second question, but what about [1.9999....] = ?

[stevex18z]

@IkonPhenom thats still gonna be one because its less than 2

[IkonPhenom]

What about [π] = ?

[ZenEskimo]

how do i plugin if its for example {{3x + 2}} ?

[jalasmith1]

what about if we square it??

for ex: x^2 + y^2 = 1

[patrickJMT]

@jalasmith1 that is a circle

[dfjndsk2008]

@jalasmith1 hahahahahahalaololol

[ZaHaTe]

thank you so much

[GamingMULE]

This kind of helped me but I'm still having trouble. thanks

[otownfever]

I friggin love you dude. The ONLY reason why I aced my Math class.

[dajavinator]

This thing is so gay, they give me on example on this in my textbook on the easiest one and then I have like 20 problems on it. O_O

[demshi1]

Very clear. Thanks bro!! I finally understood after an hour trying to figure out. U r the best ;0)

[stopableron]

wow. i spent 30mins reading how to do it from the textbook and i still dont understand it. i watched the whole 9 mins of this video and i UNDERSTAND.

[twilightfanNda123]

You're explanations cleared everything up! Thanks :D

[patrickJMT]

@twilightfanNda123 you are welcome!

[mrassbandit23]

i had a midterm where i had to graph [cosx] between 0 and pi. what should this look like?

[devedli]

what if there is a number or fraction in front of the [x] I doesn't it act almost like a slope?

[leeeeeroyjenkins1]

.99... = 1; it's 1 not 0 when rounding. just a heads up

[luKCy567]

what happens when you multiply it?

like y=[-3X] and y=-3[X]?

[patrickJMT]

@luKCy567 plug in numbers and graph it and figure it out

[charbritt1]

how do you graph if its f(x)= 2[x] -1

[1R1SHxSN1P3R]

What happens say if y=m/n[x-a]+b or what I'm trying to say is what if there's a fraction in front of the brackets and can you multiply or divide in the brackets. Thanks

[mechakinggidora]

Thank you very much! Made it a lot easier to understand, my teacher kinda skimmed over it. -_-

[hihowareyouitsme]

is there any way to make the interval between the steps more than one unit?

[aWellsie514]

We watched this is Alg 2 H class today :)

[natash179]

Can you do limit problems involving the greatest integer function?

[natash179]

I love youuuu!

[ItsTheHood]

i learned more in this 9 minute video than i did in my hour and a half class XD

[The1OthDoctor]

How do I graph f(x)= -2[x] ?

[ry7ky]

@The1OthDoctor try some values for x and plot it. You could also just use geo-gebra or wolfram to plot it for you.

[thatssoihssan]

i love you<3

[yuvrajbhatnagarsam]

thanks for this video bro.......

[nightlight12340]

I never knew how to graph these!

Thank god for this video.

[1453738]

God bless you!! lol

[EmmaWismyhero]

does multipication increase the distance of the intervals? Also, does divison lengthen the intervals?

what about those two concepts? i get them confused :/

[MsShadow1010]

sometimes they notate it like y=int(x) also. That's how it is notated in the florida edition of precalculus by sullivan and sullivan

[cjtops2002]

Thanks a lot! I was really lost from the text explanation

.

[jeevarajiit]

gr8 video thank u

[wolf92193]

You may be singularly responsible for my entire class passing calculus.

[patrickJMT]

@wolf92193 ha, tell everyone that patrickjmt says hello!

[xxmarka]

Wow. I was reading the Wikipedia article on floor and ceiling functions trying to understand what they were and it made NO SENSE. I figured it was probably simpler than I was making it out to be, but I didn't realize it was THIS simple lol. Thanks a lot.

[nickrizzo39]

what is the difference between lxl - 3 and lx - 3l

[ILoveFoetus]

@nickrizzo39 If its lxl-3 that affects whether the shift is up or down (-3 meaning 3 down, +3 three up). If its lx-3l then the graph is affected to shift left or right (-3 meaning shift 3 to the right, +3 meaning shift 3 to the left)

[ladysaiyuki09]

,great! but how about the vertical graph of the floor functions?

[aliyusuf7]

great video...thanks a million...gonna visit your channel alot...

[ItsMonAlpha]

I wish I had found this channel four years ago, before my graduating year from High School. But oh well, it's never too late! I'm sure I'll be visiting you a lot in my college years. :)

[sleepoverdia]

how do you find the domain and range for floor functions?

[afreakforplanes]

great video, thanks a lot, it really helped me

[shiningyrlife]

but here you talking about chopping off the decimal is wrong though. How about say round it down? Because if i have -2.01, i use floor function, but saying chopping off, you have -2, which is bigger than -2.01, that wrong, so saying round down is better.

[shiningyrlife]

haha I am senior in college and the definition in my discrete book make me confused about this.... even though I know it XD. Thank haha

[patr1xs]

thanks!

[KiaraLovesElissLots]

You are AWESOME. Thank you SO much!

[futebalmakedonia]

what would the domain and range be of the first example?

[futebalmakedonia]

What would the domain and range be?

[Puckosmucko]

It would be greate if you could write a book that include the theory of your videos.

[thepuppetmagician]

We went over this today in algebra 1 class and I understood it in class but once I got home I was like...uuuuuuuhh...but you refreshed my memory. THANX!

[aktebayo]

OH NO! i was so sad when it was done! I need So many more examples!! :/

[emmachu1]

what about if you have f(x)=2[[x]]? how does multiplying 2 to the floor change it?

[jennychungable]

@emmachu1 I am having the same problem. And I don't understand how it works. :/

[emmachu1]

@jennychungable I think I figured it out, what happens is the steps jump up by 2 instead of the 1 step up. So it looks the same, it just has shifted up 2 units instead of one between each elevation.  So if it were 3[[x]] then it would shift up 3 units each time. I hope that's right and that you can kind of understand what I'm trying to say? :) Good luck!

[denni0302]

@emmachu1 You're correct. Just think of it as two separate equations. Do the [[x]] first (ie. round off the number first) and THEN multiply by the coefficient - in your case, 3. If it were [[3x]] you would multiply the unrounded number, say 1.3, multiply that by 3 = 3.9 then round down to 3. So its just reversed.

[KstineCHris]

THank you!! I'm doing algebra two online, and it doesn't explain anything~ it just showed me the graph and i was like huh? but after seeing this, I'm all cleared! thank you!!

[littlealx1]

Subscribed and greatful that I did lifesaver

[MintzTape]

Wow great video! very explanatory. LOL you're a better teacher than the one at school @_@

[lovelyaria5]

Dude.. u r makin the world a better place... Thanks so very much!!! =)

[MrHushmonkey]

Thank you for your time to make this. I really do appreciate this!

[mywordpass]

I... I think I love you.

Thanks for your vid. We never covered the Floor function and bam, there it is on the homework. You saved me several distressed hours

[nonicknamekid2010]

what if you're already given a domain?

[64talb]

still confused

[patrickJMT]

@bananazx33 thanks : )

[lethaltimes]

u r definitely a math wiz!

[courtp313]

You made it wayy more clear than my teacher, I'll probably get it after watching this a few times. Thank you! (:

[shhhhhlaura]

on the y=[x-3] , why do you go to the right 3 points instead of left because it is negative ?

[shhhhhlaura]

on the y=[x-3] , why do you go to the right 3 points instead of left because it is negative ?

[DevynGrayer]

MAN YOU SAVED MY LIFE!!!!!!!!!! ^_^ I subscribed

[TehChangster]

I LOVE YOUUUUUUUUU!! ^^ [Not in a gay way XP] thanks for all your vids~! ^^

[Noviantoable]

my teacher was wrong. he rounded the number to the above number...

poor

[patrickJMT]

@Noviantoable well we all make mistakes : ) so long as he fixes it !

[McBirdec]

your website is incredible.

[patrickJMT]

@McBirdec thanks!

[poohpoohgirlsj]

HUGE LIFE SAVING !!!

[wdmzswzz]

thanks, this helped my friend a ton\

[Twilightroxs84]

wait how would you solve the greatest integer function with a number infront of x? such as [3x] - 5?

[cod4mp5addic]

Hey man thanks so much for this! it really helps keep it up!

[ProjectCivil]

You're a hero.

[disteen]

Thank You So Much! Your video really helped answer my questions =D

[311fran311]

your videos are very useful, thanks!!

[jasonc952000]

THANK GOD FOR PEOPLE LIKE U

my teacher blows at teaching all we do is take notes and he speaks like a monotone retard thank YOU!!!!!!!!!!!!

:D:D:D:D:D:D:D:D:D:D:D

[ferrari2o17]

alright if its y=[2x] it changes the slope but i dont get why the horizontal lines are like from 0 to .5 then 1 to 1.5 then 1.5 to 2... cant i just do 0 to 1 then the slope is up 2 then right 1 then thats where the 2nd line starts? do u kinda get it

[theArbitrarychannel]

Wow- Here I was almost FAILING my math class and now... I watched your video and everything's so much clearer! thank You SO MUCH! :D

[patrickJMT]

@theArbitrarychannel glad it makes sense now

[munish00789]

he is a saint.

[qo1o4262UYA]

lol the 2nd and third example were the exact same ones on my hw thnks for the help

[SLTrider17]

Im learning algebra 2 through you. Thank you.

[clarinet11]

I'm stuck with a crappy precal teacher, and she made this look harder than it is. Thanks a lot! Really helpful. :)

[patrickJMT]

@clarinet11 glad i could help : ) i am always here ....

[cenacrazed544]

@clarinet11 me toooooo!

[fcbai8]

How would you find the range of a greatest integer function that has been dilated/reflected/translated

ex: -2*[2x]+1 i know that the domain is all real numbers but im confused about the range because i guess that the even y valies are not included after graphing it please help

[BarbieDorn]

hi there patrickJMT i knw the right person to solve my assignment please patrickJMT can you show how to graph this f(x) = x + 1/2 and the other one is g(x) = 2 - x ... i really really need your help. i can easily understand u video.

thank you so much

[azerbaijan93]

Thanks alot man! It was so blurred till I saw your vid. Thanks!

[metalshadowmario4]

I did this for 2 months and I didn't get it. I watch a 9:05 minute long video the day before my exam, and it finally clicks. Thank you for being so clear and easy to understand!

[hambagman]

1 problem with this video i though if u have Y=[x-3] you move it to the left of the graph.

[poplop95]

wow.... i really like your explanation and it helped me. can you give us more samples? my teacher always giving easy samples during the lecture but whenever we are having a test.. he always gave us difficult questions.. pls help me.. thanks :))

[TheHosecloth]

Fantastic Explanation! Just what I needed to finish my homework. You are amazing! And you're helping struggling upperclassmen everywhere.

[hermionegranger180]

Wow! you did a better job than my algebra teacher!

[harfang2143]

good job man

[kbt1993]

how come he doesn't round 0.5 to 1?...

i dont get it

[dsvoid]

@kbt1993

You round DOWN despite the "greatest" in the title.

[iceobreakers]

@kbt1993 [0.5]= 0 not 1

[tops4jesus]

good job men really

[asanesss10]

thanks ^_^

[aparrotslife]

Patrick, you are one of the best gifts I've ever had in my schooling! It seems as if I watch your videos after I come out of my math class each time. You help reinforce what I learn in class.  You are amazing; I wish you were my actual classroom teacher. You are indded a lifesaver. Thank you very, very much!!! :)

[Theabdullahzaib]

thnx a lot!

[lawliet110]

You're AMAZING!!!

[Saverick8]

This really really helps!!

Thank you!!

You're amazing!!

[Makissy13]

your awesomee !

thankss !

i totally understand noww :D

[Murfitizer26]

saved my ass. i got a test on this tommorow

[kjmoney007]

thx i understand now btw y r u trying to sell this? ppl just use youtube downloaderz

[NaruIchiLuffy]

Man u just saved me :P U ROCK

[biboooy1]

thanks men!! I can do my report now..thank you so much!

[HersheyKiss23]

Thank you so much! This helped me soo much with my Algebra 2 homework! You're amazing!

[rainbowloretta]

thank god someone will teach me my teacher doesnt teach us she just says read the book the book = epic fail as a teacher haha

THANKS!!!

[KinkyCaution]

This video helped me so much not only in translation, but also in clarifying why the pattern turns out to be a staircase-type. Thank you! Keep up the good work.

[patrickguo]

Ehhh... It says here in my Calculus book that "The Greatest integer Function is defined by [[x]] = the largest integer that is less than or equal to x" soo when you said when x = -99 y is also supposed to be -99

[hafizschoolwork]

if your asking about the the first problem he did, y = [x] then he actually meant when x=0.99 then y=1. but yea ur right when x= -99 then y=-99.

[DeathMagnetic90]

Thanks A LOT! Really help me alot. Keep posting videos, you're doing a great job.

[taynahmalinsky]

you saved my life! THANK U SO MUCH =D please keep doing more videos!

[cuterz2007]

tnx so much.. this one i can rewind, my teacher, i cant... :D

[lorrz115]

i remember when our tchr taught this.. it was so confusing! not until i've watched this.. THANKS ALOT!! :D

[savages9]

i finally learned this...

i had a headache and the school nurse sent me back to class and i missed most of it...

u saved me from failing...

thx..

[TheSkinnySpencer]

With PatrickJMT, going to class is a complete waste of my time lol

[szzd]

ohhh urr a greatt helpp...... wattt iff the question was f(x)=-2[[x]] and i had to find the y-intercept and the xinterceptt and i had to graph and find domain and range

[anji0san]

I understood in less than ten minutes what I couldn't in more than 30 minutes, thank you so much !!

[xsteeneezy]

you are a life saver.

[ChiBulls23MJ]

Thanks Man! This is great.

[randomobsessor]

thank you sooo much for posting this!!!when i first learned this in class, it looked to me like numbers with bars around them lol. but now i get it and this should deffinately help with my test on wednesday.

[mongoose308]

Being able to rewind helps too lol.

[patrickJMT]

yes, this is very much a luxury of the digital age!!!

thanks for the nice comments : )

[mongoose308]

Your videos are awesome! I'll actually pass my test on Friday. Your videos are good becuase you give alot of easy to understand examples and you don't rush. I learned more in Nine minutes than I did in 35 minutes(in school) lol.

[RayChellz]

Thank you so much for this! i have a test on it 2morrow...i'm gonna ace it!

[patrickJMT]

oh yea! good luck!!

[89Critic89]

Excellent!

[RingedGodspeed]

this video helped me get a better understanding of the greatest integer function, thanks. But could you help me limit problems that incorporate the greatest integer function. for example: as the limit of x approaches 7/2 from the right side int(2x-1). I dont know how to proceed to solve that question. Any help would be appreciated.

[KillaDaedalus]

Thank you for posting this! My textbook was not very clear in its explanation, however, any doubts I had on this topic are now resolved. Thanks again!

[patrickJMT]

excellent! glad it helped!

now just remember not to fly too close to the suN!

[calculus100]

Amigo, muy buena explicación. Desde Venezuela. Muchas gracias.