Advanced Functions 5.3 Graphing Rational Functions with Oblique Asymptotes

We also take a look at holes in the function.

[amyl]

This chapter is harder than previous ones. Followed your channel (so helpful) watched a few times, pass through with no issues. BIG THANKS :)

[taiyoko]

This has helped me so much! Words can not describe how thankful I am for you!! Keep posting these math videos they are so helpful

[abigailstar]

hello how would you solve the oblique asymptote when for example x^3/x^2+1, I did x^3/x^2 + x^3/1 and I got x + x^3 but apparently the equation of the o.a. is y=x

[jonathanzhang]

do you have any textbook homework questions along with the lessons or is it just the lessons

[hollowayfan]

What happens if you’re dividing by more than just x though?

Like (x^2 + 5) / (x -4)

Now you can’t just divide each term in the numerator by x, so what do you do?

[jamesviola]

For 5:04, example 2, how is it that expanding got them x^3 -3x -2, wouldn't the remainder be +2? I even typed the equation into google & it said expanding it would make it x^3 -3x +2. Am I missing something?

[sovxyzero]

How would i solve if there was vertical asymptote for example (x^2 + 2)/(x -6)

[ammarkhan]

Hi, Ms. Havrot love the videos and have learned a lot. I had one question about graphing so how do you estimate the scale to use?

Because when I basically finish my whole graph and its in small intervals. When the question asks me for a test point to determine local/max points i do that last. And what ends up happening is my y value is way too big for my scale to fit it so I have to basically regraph everything which isn't efficient for a test or something.

Another question I had was for the test points let's say I have 1 vertical asymptote and 1 Oblique parabola asymptote, and f(x) ends up being a parabola in between the two how would I predict the test point to use to best find the local max and min. An example i was doing that had this exact question was x³+3/x-1. And is it wrong to choose a test point and that test point ends up not being the actual local max or min. Sorry for the amount of questions its just these 3 have really been confusing me. I'm good with the graphing and everything else.

Thanks