My teacher taught us how to find vertical & horizontal asymptotes (something i already understood) but just threw us into the deep end on slant asymptotes and long division (something no one knew how to do)
Because teachers were not just people who teach, they have additional and bonus works unlike for tutors who only study and teach and make videos but yeah teachers were not the best at teaching
Love your videos! On your second example, I factored out a - 1/2 from the denominator and then did the long division. Then you don't have to deal with fractions while dividing. Then, I multiplied the answer 3x by -1/2 to get the slant asymptote. You can also multiply the remainder by - 1/2 if working a different type of problem.
I really liked that you chose coefficients that would produce a fractional quotient, made it harder and prepared me better for upcoming test. Great job!
With all the cuts to my local community college, I'm suffering through some really bad, brand new teachers. You are my savior, any concept that I have trouble with I know I can count on you to save the day. Thank you so much!
THANK YOU SO MUCH! your work is greatly appreciated. my math teacher is also a basketball coach so when he teaches he teaches in a "short cut term" way ("go here, do that, and BAM! there you go" type way.lol) but you talk with smoothness. in a simple way but not too slow. I dont even have questions bc of your thoroughness and you could did this in only 10 mins. makes me wonder what i do for 50 mins. 5 days a week with no bathroom breaks. THANK YOU SO MUCH. your keeping my dreams alive! :)
Yeah, they tell you to find the minimum and maximum point. But that makes it so much more complicated for something as simple as a "sketch the graph" question -_-
You're formatting for the videos is awesome! With both the whiteboard and paper. Great job, this helped clarify a lot going from equations to the graph.
Thank you. I really wish math was taught like this more. my book is horrible and my teacher just seems like she wants us to fail. Thank you very much you are doing a good service with these videos.
@patrickJMT you've saved me! thanks! he's talking about the rare case when a line can cross over the horizontal or slant/oblique asymptote (but never the vertical). once f(x) crosses the asymptote though, it will never go back over. im just having difficulty finding when it will cross over.
ghostlygangsta as a freshman!?!?! Dang dude..In Arkansas (49th in education :D) has 8th graders taking algebra 1 if you took the pre ap course and then geometry in 9th if you continued in the pre ap course. And then your sophomore year you take Pre-Ap Algebra 2 (if you kept going the advanced course) Good luck m8. You'll be so much more advanced as I am.
+ghostlygangsta Yeah, algebra 2 kids don't learn asymptotes, nice try. Also honors? If you would have said GT a slight chance, but honors?! That is very hard to believe because I took Honors algebra 2 myself in freshmen year. You start to learn about asymptotes in the United States when you are in College Algebra/ Algebra College. A freshman taking College Algebra would fit your case, but sine you said algebra 2 that is very hard to believe. Also, you have learned y=mx+b in 6th grade? What you are saying is you took algebra 1 in 6th grade, yet you are in an honors algebra 2 class as a freshmen that is learning asymptotes? Once again your statement is false kid.
@restockermaster well, divide the highest power in numerator by the highest in the denominator; the rational function will resemble this graph for values of x that are large in absolute value
Just an little helping point - you put your second half of the graph on top of the asymptote when it should go under the slant asymptote and approach the vertical asymptote
You say asymptote funny, lol - Seriously though, you're awesome for doing this, I was helping my sister with pre-calc and this was the only thing holding me up. Thank you very much for posting this.
in terms of finding the asymptote, no, it has no significance except that as we take the limit, that part will approach zero. of course, algebraically its significance is that without it, we would not have the same original function but again, we do not need the remained to find the SA
Thankyou very much yet again Patrick i was absent for the day my teacher taught us these horizontal vertical and slant asymptotes and the graphing of it(ive seen the other vids, just wished to comment on the first) il do so on the others as well:D Now i just have one question! Will you ever consider private tutoring me if i would ever need it?:D
typically with end behavior, people just discuss whether it approaches a horizontal asymptote (the number), or whether it approaches infinity or negative infinity. however, i do not see why you could not say it approaches the slant asymptote. i would check with your teacher to see what they want. technically either is correct. i do not think there is a hard and fast rule. if there is, i am unaware of it.
Hi Sir, i know these videos focus on the shortcut to find the asymptote, but is it correct, in your 2nd example, the vertical asymp are -sqt2 and sqt2?????thanks for this video....clearly explained and so simple : )
Can you have more than one oblique asymptote? How would you find these? What if the numerator is more than one degree higher than the denominator? Thanks for the videos, they make everything seem so simple!
@patrickJMT I think he is talking about how certain functions actually cross a horizontal asymptote. Everyone in my class thought you can't "touch" or "cross" hor asym. But you can in examples of sine functions... or even simple ones like y = (100x)/((x+2)^2) i think....
SWAG, checked this out right before my calc test tomorrow, graphing functions by hand, finding asymptotes, concave up/down, first and 2nd derivatives came easy... except I didn't know how to find slant asymptotes... lol
ohh, i see.. anyways, one more question.. so when you're asked for the end behavior, would you say that as x -> infinity, f(x) -> slant asymptote, or infinity?? like would you say f(x) -> -3/2x OR f(x) -> infinity, when you are asked for end behavior?
excuse me, in my university they say that: to find a slant asymptote "ax +b" you find "a" as the limit as x approaches infinity of f(x)/x and to find "b" is the limit as x approaches infinite of f(x) - ax but when i use this method in the first example i get -3/2x + 0 can you make some videos using this or at least tell me if i'm doing something wrong?
@matheusscaj You cannot always use synthetic division because synthetic division is only used to divide by a linear function (for example, x-1). For the first example, you could use it but the other 2 functions you could not use it as they are exponential functions and are not linear.
I just realized that sometimes tutors, like you, are better teachers than "teachers" themselves
Antonio Jesus Tutors > Teachers.
to me he is not a tutor he is an awesome professor ! :)
My teacher taught us how to find vertical & horizontal asymptotes (something i already understood) but just threw us into the deep end on slant asymptotes and long division (something no one knew how to do)
Because teachers were not just people who teach, they have additional and bonus works unlike for tutors who only study and teach and make videos but yeah teachers were not the best at teaching
You're saving my life rn
my engineering career saved :D
Love your videos!
On your second example, I factored out a - 1/2 from the denominator and then did the long division. Then you don't have to deal with fractions while dividing.
Then, I multiplied the answer 3x by -1/2 to get the slant asymptote. You can also multiply the remainder by - 1/2 if working a different type of problem.
That's a nice way of doing it 👍🏽
@@hrperformance Thanks!
I really liked that you chose coefficients that would produce a fractional quotient, made it harder and prepared me better for upcoming test. Great job!
With all the cuts to my local community college, I'm suffering through some really bad, brand new teachers. You are my savior, any concept that I have trouble with I know I can count on you to save the day. Thank you so much!
THANK YOU SO MUCH! your work is greatly appreciated. my math teacher is also a basketball coach so when he teaches he teaches in a "short cut term" way ("go here, do that, and BAM! there you go" type way.lol) but you talk with smoothness. in a simple way but not too slow. I dont even have questions bc of your thoroughness and you could did this in only 10 mins. makes me wonder what i do for 50 mins. 5 days a week with no bathroom breaks. THANK YOU SO MUCH. your keeping my dreams alive! :)
If I pass Calculus you will be the reason why. Thank you for existing!
You, sir, have my respect. You are writing on a white board left-handed without smudging, something I have not yet mastered.
Oh man, this was super helpful. Idk why Pearson couldn't have just said it that way to begin with...Thanks!
Yeah, they tell you to find the minimum and maximum point. But that makes it so much more complicated for something as simple as a "sketch the graph" question -_-
You're formatting for the videos is awesome! With both the whiteboard and paper.
Great job, this helped clarify a lot going from equations to the graph.
i felt like a complete mess until i saw this. somehow you just made things 100% simpler. i applaud you! thank you soo much for your channel and work.
Thank you. I really wish math was taught like this more. my book is horrible and my teacher just seems like she wants us to fail. Thank you very much you are doing a good service with these videos.
Thank you so much dude. You just helped me with an 8 point problem on a test within 50 seconds. You are the shit!!!
dude...i love you patrick saved my homework grade and MY LIFE
Thank you for teaching me more math in one night my professor could in a semester. I applaud you, sir.
You are awesome I can't tell you how many time I try to understand this by reading the text book. Thank you so much
@patrickJMT you've saved me!
thanks!
he's talking about the rare case when a line can cross over the horizontal or slant/oblique asymptote (but never the vertical). once f(x) crosses the asymptote though, it will never go back over. im just having difficulty finding when it will cross over.
oh my god, thank you. I have my calc final tonight, and this is on it, and my prof never TOUCHED on it. You may have just saved me a mark. THANK YOU!
I have a pre-calculus review exam in a few hours, I learned this so long ago and had no idea how I would pass the exam, Thank you so much!
@sohumd96 the remainder will go to zero as you take the limit at infinity (or negative infinity) so yes, you can ignore it
I'm a freshman in high school doing honors algebra two and I don't think I'd be passing if it weren't for your videos. Thank you so much.
Damn, we're learning this in grade 11 in Canada. When I was a freshman we were just doing y=mx+b. I can't even imagine your workload D: Good luck :)
haha thanks i wish i could go back to slope intercept form sixth grade was the best XD
ghostlygangsta as a freshman!?!?! Dang dude..In Arkansas (49th in education :D) has 8th graders taking algebra 1 if you took the pre ap course and then geometry in 9th if you continued in the pre ap course. And then your sophomore year you take Pre-Ap Algebra 2 (if you kept going the advanced course) Good luck m8. You'll be so much more advanced as I am.
+ghostlygangsta Yeah, algebra 2 kids don't learn asymptotes, nice try. Also honors? If you would have said GT a slight chance, but honors?! That is very hard to believe because I took Honors algebra 2 myself in freshmen year. You start to learn about asymptotes in the United States when you are in College Algebra/ Algebra College. A freshman taking College Algebra would fit your case, but sine you said algebra 2 that is very hard to believe. Also, you have learned y=mx+b in 6th grade? What you are saying is you took algebra 1 in 6th grade, yet you are in an honors algebra 2 class as a freshmen that is learning asymptotes? Once again your statement is false kid.
Prodigy Fumar I did in my pre-ap algebra 2 course as a sophomore. We even learned how to calculate slant asymptotes.
@restockermaster well, divide the highest power in numerator by the highest in the denominator; the rational function will resemble this graph for values of x that are large in absolute value
Just an little helping point - you put your second half of the graph on top of the asymptote when it should go under the slant asymptote and approach the vertical asymptote
These are great!! thank you so much! You are saving my college algebra career.
Thank you. I appreciate all your videos. They really do help.
your videos really help to refresh my memories and even teaches me stuff I didn't know before...thanks alot
Jesus christ, That was so simple. Thank you.
You say asymptote funny, lol -
Seriously though, you're awesome for doing this, I was helping my sister with pre-calc and this was the only thing holding me up. Thank you very much for posting this.
Super work dude! I will look for more of your videos when I need help doing homework. My math teacher sucks big time.
Dude, you are a straight up BALLER!!!
Thanks for being awesome man!
no prob my man.
good luck in the class
This is one of the videos that definitely helped me, so thanks a lot! :)
Patrick, I think I speak for a lot of people when I say this; you have saved our asses in math too many times...
saved me. i always cram right b4 tha test but this time i was stuck, now you bailed me out....test 2maro! YAY!!!
Really needed this thanks man. Keep up the good work.
proved youtube has educational uses to my parents.
thanks so much :]
You're better at teaching than my pre cal teacher. Thanks :D
you explain better than my teacher too! ty
Thank you so much, so much easier and to the point. Now a subscriber
Your videos really do help. keep it up.
Lennon del tanbor
WHO EVEN NEEDS TEXTBOOKS!! U ROCK PATRICK!!
thank you for you're video it really helped. This was the only thing that i found of slant asymptotes that i could understand :)
PatrickJMT is a PROFIT from the math gods.
YOu explain this so much better than my teacher
this helped me to do advanced calculus in 2021! Awesome.
this is a really good video...you keep my attention throughout it...wish my teacher did that
tanks to u patrick for taking ur time to breing out dis video
Great videos! better at helping me learn than my teacher, i would also show synthetic substitution because that is how i learned.
You are a GENIUS and a LIFE SAVER. THANK YOU!
Simple and great videos Patrick!
Big help for my Calc test tomarrow
Lol glad I finally learned how to do this. Have a math final tomorrow! WISH ME LUCK ILL NEED IT.
good luck!
I love all of your videos!! Thank you so much!
Great video. I really understood SA's after watching it
Thank you!
I was looking for this last week, but i can use this as reference now :)
Patrick, does this condition apply only when the degree is ONE larger? not two or three correct?
yea man
no. not correct. These are slants. the higher the degree the higher the degree of the asymptote
Yes, but for an asy with degree one ( a line), you need to have (x^n)/(x^(n-1))
I understand this more than my teacher. Thank you
in terms of finding the asymptote, no, it has no significance except that as we take the limit, that part will approach zero.
of course, algebraically its significance is that without it, we would not have the same original function but again, we do not need the remained to find the SA
Thank you very much! I have take-home test and this helps me a lot!! =))
dude i love your videos i would fail pre-cal without you lol
@johnmichaelsaren only if you are dividing with a linear factor
lmao the two examples you did were on my homework
thnx :)
Thankyou very much yet again Patrick
i was absent for the day my teacher taught us these horizontal vertical and slant asymptotes and the graphing of it(ive seen the other vids, just wished to comment on the first) il do so on the others as well:D
Now i just have one question!
Will you ever consider private tutoring me if i would ever need it?:D
hi patrick.. i love you! thanks for making my life easier
Very clear! Teaching rational functions to human beings (who often function irrationally) is a challenge.
typically with end behavior, people just discuss whether it approaches a horizontal asymptote (the number), or whether it approaches infinity or negative infinity. however, i do not see why you could not say it approaches the slant asymptote. i would check with your teacher to see what they want. technically either is correct. i do not think there is a hard and fast rule. if there is, i am unaware of it.
SAVED lol, I hadn't done polynomial long division in a year and it just pops back up and clotheslines me.
Cool video! But could you explain why exactly does the long division give the oblique asymptote?
Is there a way to determine if a slant asymptote exists without doing the long division? I'm trying to conserve time on tests.
The slant asymptotes only exist when the degree of the numerator is one larger than the degree of the denominator.
ex: x^3/x^2
not ex: x^3/x^3
A way to find the slant asymptote? Use synthetic divison instead of long.
Then a slant asymptote dne
Nothing.
Ok that has vertical asymptote of zero. It's easier to see if you add like a 4.
Your videos really help! Thanks so much.
thank you so much.. but i have one question.. why does the first example have a vertical asymptote at x=4? thanks for everything
Hi Sir, i know these videos focus on the shortcut to find the asymptote, but is it correct, in your 2nd example, the vertical asymp are -sqt2 and sqt2?????thanks for this video....clearly explained and so simple : )
Hey man, thanks. I've been looking everywhere for a synthetic division example.. fianlly found it.
Has helped me on tomorrow's test
yep
Can you have more than one oblique asymptote? How would you find these? What if the numerator is more than one degree higher than the denominator? Thanks for the videos, they make everything seem so simple!
thank you man your videos are very helpful
I'm still learning the simple stuff; Is "slant" asymptotes synonymous with "oblique" asymptotes or are they different? Thanks.
@patrickJMT I think he is talking about how certain functions actually cross a horizontal asymptote. Everyone in my class thought you can't "touch" or "cross" hor asym. But you can in examples of sine functions... or even simple ones like y = (100x)/((x+2)^2) i think....
Do you recommend always using long division when finding slant asymptotes?
Thank you! You are saving me from failing math exam!!!
OMG that was exactly what I needed! Thanks!
I was wondering if theres an easier way of doin it tho.. lol
SWAG, checked this out right before my calc test tomorrow, graphing functions by hand, finding asymptotes, concave up/down, first and 2nd derivatives came easy...
except I didn't know how to find slant asymptotes... lol
@matheusscaj i do not remember saying you can not
These are so helpful. You're great!
@jonnymartz i have videos on graphing rational functions where i actually graph it all out, so you may check out one of those
ohh, i see..
anyways, one more question.. so when you're asked for the end behavior, would you say that as x -> infinity, f(x) -> slant asymptote, or infinity??
like would you say f(x) -> -3/2x OR f(x) -> infinity, when you are asked for end behavior?
Thanks! this helped a lot and the video was good. thanks a lot.
This video was very helpful. Thank you!
jsmart1000
excuse me, in my university they say that:
to find a slant asymptote "ax +b" you find "a" as the limit as x approaches infinity of f(x)/x
and to find "b" is the limit as x approaches infinite of f(x) - ax
but when i use this method in the first example i get -3/2x + 0 can you make some videos using this or at least tell me if i'm doing something wrong?
thanks
I understand there are vertical, horizontal, and slant asymptotes. Are there any curved asymptotes?
Hi I have a quick question. When you are doing f(x) when x
@matheusscaj You cannot always use synthetic division because synthetic division is only used to divide by a linear function (for example, x-1). For the first example, you could use it but the other 2 functions you could not use it as they are exponential functions and are not linear.
Also known as the Oblique Asymptote.
Prodigy Fumar thanks XD
Thank you for the clear explanations
Thank you so much, easy to understand
you are a life saver! Thank you very much!
This is very helpful. Also, I appreciate you showing us the placeholder trick. This makes this method click for me.