How do you graph a rational function with asymptotes

👉 Learn how to graph a rational function. To graph a rational function, we first find the vertical and horizontal or slant asymptotes and the x and y-intercepts. After finding the asymptotes and the intercepts, we graph the values and then select some random points usually at each side of the asymptotes and the intercepts and graph the points, this enables us to identify the behavior of the graph and thus enable us to graph the function.
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Organized Videos:
✅ How to Graph Rational Functions
• How to Graph Rational ...
✅ Graph Reciprocal Functions | Learn About
• Graph Reciprocal Funct...
✅ How Graph the Reciprocal Function
• How Graph the Reciproc...
✅ Find the x and y-intercepts of a Rational Function
• Find the x and y-inter...
✅ How to Graph Rational Functions with Asymptotes
• How to Graph Rational ...
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#rationalfunctions #brianmclogan

[@shamalusmith2988]

For this example shouldnt you have a slant asymtote since the degree the numerator is larger than the one in the denominator?

[@brianmclogan]

yes!!!!! not sure how I missed that, the hyperbola on the left will turn down instead of continuing up. Thanks for noticing and letting me know.

[@shamalusmith2988]

Ok Your welcome

[@hamadrashid9990]

You graphed it correctly in the video, it has a quadratic asymptote (x^2+x+1)

[@andyyang3490]

Brian McLogan slant occurs only is b is less than a by 1, so you right

[@-smp-scientificmethodpersp838]

kzbin.info/www/bejne/e5DccqeiiJaFptU This is his other video on that

[@notfunny6369]

This is it chief. 45 minute class for a week and a half and I didn't learn a thing. 1 video and its all clear

[@zane5477]

Saaaame

[@bouggyman180]

ADHD gang rise up

[@hayleyjohnson2930]

wow... my teacher has been trying to teaching this topic for like 2 weeks and this video taught me in 7 minutes... if i had a teacher like this maybe i wouldn't have to stress so much

[@brianmclogan]

you are very welcome! happy to be able to help you out!

[@hunterh7778]

Swear I was just thinking that but you already said it😂

[@cxlcius1339]

I'm in 8th grade and I'm taking college classes for math and writing. I have an exam later today and I wanted to study and make sure I know all of my answers. I was a little confused with what my teachers were saying about graphing rational functions. When I look at your videos, they seem to clarify everything I should have learned from school. Thank you so much for these vids! Keep them up!!

[@brianmclogan]

you are very welcome! happy to help!

[@jonathanchacko1053]

What is the program you're in called?

[@RiceCubeTech]

They do teach this in college algebra not just alg 2

[@meganwaldrop3556]

This helped me out so much, I understand this so much more now

[@wellwisher832]

He did well. But he didn’t explain how the final graph is drawn. He plotted only two points and He rushed by drawing it without explaining.

[@englishlife5838]

Agree

[@DarkPrincess_M]

Right

[@hihellow6185]

Thank the gods for this man

[@JakeD567]

Thanks bro. This is super helpful

[@Dirthawker611]

Thank you!

[@blossom6265]

Why can't I get over that beat at 0:58 ??

[@matterthree5737]

jingle bells lol

[@neelsharma3]

Wish there were more teachers like you

[@melaniesabillon2417]

bless your soul i finally get this

[@ruwansanjeewa5420]

Thanks sir 🙏

[@-smp-scientificmethodpersp838]

Thanksgiving for including the x and y intercepts

[@drewyoung3814]

0:59 I hear jingle bells

[@juliettej0356]

I hear "Fashion show, fashion show, fashion show at lunch"

[@drewyoung3814]

Juliettej03 I don’t get it

[@juliettej0356]

@@drewyoung3814 Its from the office

[@gualterguai]

@@juliettej0356 wow u are not funny

[@juliettej0356]

@@gualterguai Wow I can't find where I asked

[@jelsiyavictoria2032]

Tanq sir it is very useful

[@sidfn1636]

Very good video I learned a lot

[@brianmclogan]

awesome! happy to be able to help you out!

[@m2tdev]

Teaching sketching graphs without using derivative must be hard. For that reason at the last part he had to give arbitrary values to sketch the graph.

[@cyrelleannedumalag5494]

I was like freaking out awhile ago in our general match class 'coz I don't know what to answer and now I'm totally freaking out because I already understand the half of it lol. Thank youuu

[@brianmclogan]

you are very welcome Cyrelle!

[@cyrelleannedumalag5494]

wow didn't expect that you'll notice my comment. Anyway looking forward for me to understand the inverse of a function

[@brianmclogan]

of course, I have plenty of examples on inverse functions as well. Keep up the hard work!

[@kammckee8123]

I wish you were my teacher, mine goes so fast and it’s impossible to keep up and I’m only a freshman

[@HardWorkPays0ff]

My professor has us find the "extent" of the graph and says that for HA asymptopes, if the numerator is greater than the denominator then the quotient of a(x)/b(x) is thr asymptope. How is this possible?

[@bodhisattva2348]

I don’t get how he got that 0-1 is = to 0. 🤯🤯🤯

[@emmanuelbelison3063]

0X1

[@denniscolaianni5678]

Nice video! How old are your students in this class?

[@brianmclogan]

probably algebra 2 or pre-calculus

[@arnavmangal2774]

If you don't have a graphing calculator and you have the intercepts and asymptotes of the graph, is there an easier way to find the direction of the graphs rather than finding each point?

[@brianmclogan]

Not that I can think of, set denominator equal to zero for vertical asymptote and plug in zero for x to find y-intercept and set numerator equal to zero to find the x-intercept

[@arnavmangal2774]

thank you!

[@hannahrutledge7053]

Im confused on what order I should do it in that would be easiest to remember how to do this. My pre calc teacher wont help me at all. I dont know how to find holes in graphs, or what to do with them

[@brianmclogan]

Simplify the rational expression first. If factors with x divide to 1 then there is a hole at the value x that is equal to 0. If that does not happen like in the example of this video then there is a vertical asymptote for all the x values that make the denominator equal to zero, hence VA at x=1

[@emmanuelbelison3063]

how we get the f(-1)? plzz answer thizz

[@pupleangel135]

how do i know which numbers to plug in for f(x)?

[@brianmclogan]

I typically pick two points to the left and right of the vertical asymptotes, keep picking points till you have an understanding of the graph

[@pingpong3311]

The function x²+x+1 is a slant asymptote for this function

[@DarkPrincess_M]

The numerator is greater than the denominator by 2 degrees...How does it supposed to have a slant asymptote? (Confused 🤔)

[@pingpong3311]

@@DarkPrincess_M If the degree of the top is greater than the degree on the bottom, there is a slant asymptote. Greater by 1 - linear slant asymptote Greater by 2 - quadratic slant asymptote Greater by 3 - cubic slant asymptote And so on.

[@DarkPrincess_M]

​@@pingpong3311 If greater by 4, what do we call it then? Also, thank you for the reply

[@pingpong3311]

@@DarkPrincess_M Quartic

[@DarkPrincess_M]

@@pingpong3311 ok thank you

[@goldenrevolve5366]

How do I find the domain and range?

[@brianmclogan]

Here is one playlist I have kzbin.info/www/bejne/qofPeZ-coJqqoZI

[@yehetohoratforeveryone8355]

What if the degree is a(x)

[@pingpong3311]

If a(x)

[@matterthree5737]

0:58 🎶

[@jagratigoyal5544]

here the slant asymptote is x^2??

[@manjumishra1896]

In which class we study this

[@lesibadaniel8398]

how about the slant or oblique asymptote ?

[@brianmclogan]

I have tons of examples, just search my channel

[@pingpong3311]

Slant asymptote = x²+x+1

[@tommitev3004]

If i see one more comment saying "WOW Brian taught me in 10 minutes what my teacher couldnt do in an hour" I will explode ffs

[@ayham_97]

2:52 Where did the (x-1) on the left side go?🤦🏼‍♂️

[@brianmclogan]

0 times (x-1) = 0

[@Nemer115]

what grade is this?

[@brianmclogan]

high school 10-12th

[@Themnem948]

Duh hello!

[@raffymusa8270]

How do you get that f(-1),f(2),f(3)

[@brianmclogan]

I made them up, helpful to pick points to the left and right of the vertical asymptote/s

[@habanaseanderickm.3813]

This one isn't from 2006 lol

[@goldenbarbie8237]

shouldn't it be positive one at 5:03 ? -1 x-1 is 1?

[@brianmclogan]

-1-1 =-2 you owe me a dollar and borrow another

[@goldenbarbie8237]

Brian McLogan ohh you are not multiplying ? Why would you subtract and not multiply

[@brianmclogan]

x-1 is subtraction even when you plug in -1 it is still subtraction (-1)-1

[@Pharomid]

I thought that too, the parentheses threw me off.

[@user-cf5lb4hc1k]

وش هذا ...😯😯😯😯😯

[@Brandonator24]

Nothing about oblique intercepts? That's what is screwing me

[@brianmclogan]

oblique asymptotes? Here is more examples kzbin.info/aero/PL0G-Nd0V5ZMq4iIakM1Vhz3sZeMU7bcCZ and kzbin.info/aero/PL0G-Nd0V5ZMrL9iQ1eA9gWo1vuw-UqDXo