Graphing a Rational Function that has an Oblique/Slant Asymptote and a Vertical Asymptote

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! Graphing a Rational Function that has an Oblique/Slant Asymptote and a vertical asymptote. One example!

[@patrickjmt]

@hermin0000 if my picture over your bed or something?

[@patrickjmt]

@jdmk20aek nope (although i used to teach)

[@patrickjmt]

@Aneurythmic yes, i realized that!

[@rhejeanlozano4280]

You forgot your hole. Which will lead to graphing errors.

[@thisabsolutegarbage]

Thank you so much for uploading this! I missed school on the day we learned this in Pre-Calculus; I hope I pass the test next week

[@NikoWheels]

You = the reason I sleep so well at night

[@katiforbes1194]

Haha 9:53 with subtitles :)

[@patrickjmt]

@ThePsionicMatrixTM lol, not quite

[@MonicaBryant]

I still don't understand how you graph a slant asymptote. What does y=x-1 even look like?? How do I know if it's positive or negative? How do I know how far up or down it crosses the y-axis? So confused!!!!

[@patrickjmt]

thanks :)

[@KrystalSquirrel]

I think in the beginning it is just easier to simplify the rational expression all the way by factoring, this would save half the time of this video. the numerator is x³ + x² -4x - 4= (x³ + x²) -(4x+ 4)=x²(x +1) -4(x+ 1)=(x+1)( x²- 4)=(x+1)(x+2)(x-2) Divide by the demoninator of x²+x-6=(x+3)(x-2)

[@lexinaut]

Asymptotally helpful video. There is an interesting shortcut possible here. The numerator can be factored by grouping which happens to work nicely here. x^3+ x^2 -4x -4 = x^2(x+1) - 4(x+1)= (x+1)(x^2 - 4)= (x+1)(x+2)(x-2). Quirky! May the Math be with Us!

[@morrissamuelYT]

Also analyzing the first derivative would show where the function is increasing or decreasing. Analyzing the second derivative shows the rate of change of the slope of the tangent to the curve, and would therefore show where the function is concave up or concave down. Thanks for the videos.

[@Moshingrobot]

What happens if after you factor and put the zeros into the numerator, both are non zero? Is this possible? Would that mean that there are two holes? And therefore, I need to use the shocker method in order to solve. Just kidding about the shocker method, but seriously, guys.

[@Manishh95]

we know y=x is a slant right? because if x=1, y=1, if x=2, y=2. this is called a linear graph. its a straight, but diagonal line. this is what i do to find if it points top left or top right, i plug in points x=0 and x=1, in the case of y=x-1.

[@Tony_Hardy]

You completely lost me here. Could you do one more of these? Also, my prof uses "sign analysis" but I haven't been able to find any vids on this. Do you know anything about this, if so could you incorporate it into a video?

[@chriskim6657]

dear thatmathguy im not tired of searching videos on youtube im tired you getting in my way every damn time im trying to learn something

[@Quichey2]

You could have also factored x^2 out of x^3 + x^2 and -4 out of -4x - 4, giving us (x^2 -4)(x + 1), and then factor (x^2 - 4) as (x+2)(x-2). Just my thought about that problem.

[@Morgam06]

Couldn't you cancel a lot at the beginning because both the top and bottom factories to factors that can cancel or would that mess with the graph in some way?

[@drastichaudhari]

My teacher wants us to do it without plotting the points and do it by looking at the multiplicity and the sign change.How do i do that???PLZ HELP

[@morinkid2]

yo i watch your vids and ur very good. but on numerator if u would have factored by grouping in the first place you wouldve saved a few minutes

[@masnani58]

Hey u are a genius! Thanks a lot. Algebra 2 is kinda hard but it all comes down with practice. You should do these videos more often.

[@silentcod3r]

@4:15 you used division for factoring. Wouldn't it have been easier to factor by grouping? That seems a lot simpler to me.

[@ItsmeMaks]

u messed up last min :p -6 not 6 haha and how do u show that hole at x =2 but other then that amazing teacher good video!

[@tesslababcock7820]

I think it was meant to just simplify it as much as possible so that you can better find your intercepts.

[@Aneurythmic]

Nice lesson, however you didn't account for the discontinuity at x=2 in your final graph.

[@skateandtennis]

You are amazing, sir. Now I can fall asleep during class not feeling guilty anymore. :)

[@l2ozy]

I have a test on this chapter your video helped me a lot.... thxxxxxxxxxxxxx

[@meissathiam5193]

hey your vids re very helpful but i just wanted to know why divide by x-2

[@sk8guy500]

Would there be a hole in the graph at x = 2 because we have (x-2) on both the numerator and denominator?

[@Ocd57nZn]

at the end, the point is (-4,=6) but you accidently wrote (-4,6)

[@PSNDaSingh]

You should've just factored by grouping, takes 2 seconds.....

[@Smileystayfly1]

your the best teacher ever thank you so muchhh

[@jdmk20aek]

your videos are GREAT ! are you a professor?

[@Blackgise]

awesome, great job and thanks for video

[@thebigu01]

do we always look for x-intercepts ?

[@NyquilFriend]

This video > 5 days of algebra class

[@firered84]

i think you forgot about the hole

[@dmstefo]

i learned more in 12 minutes than i have in a week of doing this in class .thank you so much , best teacher ever !! im spreading the word of your lessons lol

[@mehn19364]

anyone realize he's left handed?

[@l2ozy]

I wish you was my teacher

[@Weejee456]

Beautiful handwriting xD

[@Nordic_Goon]

I was told not to do synthetic division in these cases because it isn't always accurate?

[@laxshooter15]

thanks a bunch bro

[@bennysmith5920]

Awesome video, you're really helping me study for my precalc test on Tuesday! Keep it up. :)

[@alecsyselse4272]

DO NOT TURN ON THE SUBTITLES THEY ARE SO EFFING WRONG...LOL

[@paulinagusciora9129]

two hours condensed into less than 13 minutes. i cannot thank you enough!

[@trlax31]

You are freaking awesome sir!!! Thanks a bunch for your help

[@heyohsurferdudes]

lefty pride

[@sphinx245]

you explained what our teacher took a week to teach, thank you!

[@eris3585]

lol 10:10 in between your what!? I beg your pardon!

[@ckzombie1130]

can a graph ever cross an oblique asymptote

[@riddickosei8977]

patrick why didnt u divide the equation by x-3 but rather x-2.. and the horizontal asymptote i had x+1/1 so how does it have no horizontal asymptote

[@VerryLongName]

The degree in the numerator is bigger than the degree in the denominator

[@ianngan5342]

why you so smart ?

[@akshinator417]

tanks

[@ailurophile4341]

Why is it oblique tho?

[@muneebali9184]

Well If Your Degree on the Norminator is + 1 Then Degree on the Denominator. Then There is Oblique.