Graphing Rational Functions With Vertical, Horizontal & Slant Asymptotes, Holes, Domain & Range

Graphing Rational Functions With Vertical, Horizontal & Slant Asymptotes, Holes, Domain & Range

Graphing Rational Functions With Vertical, Horizontal & Slant Asymptotes, Holes, Domain & Range

This algebra 2 / precalculus video tutorial explains how to graph rational functions with asymptotes and holes. It shows you how to identify the vertical asymptotes by setting the denominator equal to zero and solving for x. It shows you how to find the equation of the horizontal asymptote by comparing the degree of the numerator with that of the denominator. In addition, it shows you how to find and graph the slant asymptote / oblique asymptote using long division. This video also shows you how to identify the x and y coordinate of any holes in the graph. This video contains plenty of examples and practice problems including those in which factoring quadratic expressions and equations are involved. This video also discusses the transformations that occur when graphing rational functions. Horizontal and Vertical shifts are covered as well as reflection over the y axis and the origin. In addition, this video shows you how to the coordinates of the x intercept and y intercept. Finally, this tutorial shows you how to write the domain and range of a rational function using interval notation. It mentions when parentheses and brackets should be use. Whenever you need to write the domain of a rational function, you need to take into account the vertical asymptote and the x coordinate of any holes in the graph. For the range, you need to remove the horizontal asymptote and the y coordinate of any holes in the curve. This video might be useful for students taking calculus.

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47 Responses to “Graphing Rational Functions With Vertical, Horizontal & Slant Asymptotes, Holes, Domain & Range”

  1. Elissa Roumani says:

    I don't get it

  2. mydogissmartandwellbehaved 10 says:

    But for the first one, how do you know that the horizontal asymptote is zero?

  3. Prince Kangwa says:

    this guy deserves a medal

  4. Brianna George says:

    I’m taking a friggin quiz rn and nothing is helping me omg😭

  5. Islam dowidar says:

    11:19 (-oo,1)u(1,oo) not (-1)

  6. entertheMatriX says:

    All i see are freaking lines everywhere, hahaha

  7. Etsubdink Getachew says:


  8. Jayce Ledet says:

    Even 4 years after this was posted, this man is helping so many people, he deserves every good thing in life.

  9. ChiliWeather says:

    He taught 2 weeks of class time in less than an hour

  10. berbice25 says:

    Very helpful videos. Example f(x) = 1/x+1 Domain range shows -1. I am not sure why -1? Thanks.

  11. Team Garske says:

    Your my teacher cause my other one sucks

  12. Jason Quark says:

    I would like to thank you for this amazing 58 minutes of incredible explanation that my teacher couldnt do within months

  13. Joshh Schrimsher says:

    I am taking PreCal in college. I have a 60 right now. There is 12 assignments left and 3 tests left. Overall, 28 assignments and 4 tests. Tests count as 60% and assignments are 40%. Do I have enough time to get that back up to at least 69.50? Please, if someone could guarantee me a passing grade. I will send you $35 a week.

  14. Alejandra Franco says:

    Hello, I was wondering if you could please help me with the following exercise.
    To divide the function f(x-1) by (x^2+2x-3), we find that the quotient is Q(x) and the remainder is (x-3). If f(0)=a and f(-4)=b, what is the value of b/a? Thank youu β™₯

  15. Tech zone says:

    11:03 the domain ?

  16. peter says:

    procrastination is not my middle name.

  17. Eleni Yalew says:


  18. Everyday Life says:

    you are so freaking awsome.. this is so easy to understand.. thank you so much ….. i love it

  19. Mars Martian says:

    i'm gonna be honest, i have to do an online test today and i'm just binging all rational functions and equation videos πŸ˜€πŸ’”

  20. Dragon Dan says:

    For the last problem, I believe those local max and mins could be found by taking the first derivative and setting it equal to zero

  21. Tomato _ O says:

    thank you so much for the tutorial video, your tutorial is one of the best in my opinion, I only watch the one you updated and Khan Academy TvT The others are just not on the point.

  22. Aiden Doyle says:

    I've been trying to figure out how to find the holes of a rational function for weeks and just figured it out 37:57

  23. SohanPy says:

    Watching all 54 minutes of this video was worth it πŸ₯°πŸ‘

  24. Aselefach Mesfine says:

    Tnk bra

  25. Mahira Malik says:

    Wow , your way of teaching is extremely wonderful ,I really really appreciate your work πŸ‘πŸ‘πŸ‘πŸ‘

  26. HOWOW TV says:

    U have to change ur channel name bro not only chemistry

  27. Eddy Dormilus says:

    Those that gave O.C.T. a thumb down are truly hopeless in calculus, and they blame their hopelessness in advanced math on O.C.T.

  28. safa noor says:

    i think at 11:16 domain is (-infinty , 1) U (1 , +infinity)

  29. Franchezca Plaisival says:

    Thank youuuuuuuuuuuuuuuuuuuuu so muchhhhh

  30. Shupiwe bandah says:

    What if you are given a domain how do you graph

  31. Cayly Likes Sweets says:

    Thank you so much, I really needed this videoπŸ‘πŸ‘πŸ‘

  32. Sandra Stevehill says:

    We have an exam tomorrow😰… wish me luck

  33. Dennis Ray Rosas says:

    Is it always the numerator to be used when finding x and y intercept?

  34. Mahmoud mohamed says:

    in 24:00 I am sure that you draw a wrong graph.

  35. tgssabri says:

    You are a great help, straight forward videos, best on the internet. You are my main reference right now.

  36. Worm on a string says:

    anyone else crying in math class? πŸ™‚

  37. The gamer says:

    Life saver is explaining

  38. Mpho Raboroko says:

    I'm here to learn basics for advance math so I can understand memes, πŸ˜…. Thank you so much

  39. Gol D. Vanish says:

    Urgent! How do I know if a graf has extremepoints? For example: x/(x-2)? If in supposed to draw this graph, how should I know not to waste time on derivating x/(x-2) and setting it equal to 0?

  40. Asif says:

    This man is a legend

  41. Peter Colman says:

    what do you mean by "when want to find the domain of a function particularly a vertical Function, remove all the X-values and the VA that you have"?

  42. Quod Ambulat Lectitantur says:

    Thanks a lot this help me in guiding my son, Math is kinda hard now adays πŸ˜­πŸ˜€

  43. こうせい says:

    fuck math

  44. Emperor Vladimir says:

    The video is amazing but I just want to suggest increasing the volume of your voice. Aside that, Nice content!

  45. Luna M says:

    I started at 2 am and now it's 6 am …
    This whole time I was studying graphs and all are from your videos 😭β™₯
    Am really thankful for all what u did , u just don't know how much this means to me πŸ˜„ u r really a life saver may God bless u n ur family
    My number one hero!!

  46. Jay Zie's says:


  47. Jay Zie's says:


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