Rational Functions Graphing

How to Graph Rational Functions using vertical asymptotes, horizontal asymptotes, x-intercepts, and y-intercepts.

0:12 Example 1 Degree in Denominator is Greater than Numerator
0:48 Factoring to Look For Discontinuities
1:19 Set Denominator Factors to Zero to Find Vertical Asymptotes
1:58 Finding X and Y Intercepts
2:49 Using Sign Analysis to Determine the Behavior Near Asymptotes
5:16 Can Cross a Horizontal Asymptotes but Not a Vertical One
6:00 Example 2 Degree in Numerator Equals Degree in Denominator
6:48 Horizontal Asymptote Equal to Ratio of Coefficients
7:12 Identifying a Hole
7:33 How to Find the Y-Coordinate of the Hole
8:20 Locating Vertical Asymptote
8:30 Finding X and Y Intercepts
9:30 Using Sign Analysis to Determine Behavior Near Vertical Asymptotes
10:33 Example 3 Degree in Numerator is Higher than Denominator
11:30 Using Division to Find Equation of Slant Asymptote
12:11 How to Find Vertical Asymptote
12:20 Finding X and Y Intercepts

Related Videos:

Finding Zeros of Rational Functions

Finding Horizontal and Vertical Asymptotes

Holes Graphing Rational Functions

Slant Asymptotes Graphing Rational Functions

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[aaronjohnson]

By far the best explanation of this topic that I've ever seen.

[GuitarMAXMusic]

You're videos are BY FAR, the best math videos on YT!

[east]

Crystal clear explanation. Wow. I love the technique, sir. (I am pertaining to the sign analysis) Thank you for making this video :)

[ajbfkg]

You have been so helpful when I used to study for the SAT Math Level II and now you're helping me with AP Calculus. Thank you so much.

[OrdoArcus]

This was clutch Mr. Mario. I have a test Thursday, and I'm feeling good about it!

[sqxxklw]

You’re the best math teacher I’ve ever met.

[uhhhliza]

WOW IVE BEEN CONFUSED FOR AN ENTIRE MONTH LOL OMG MY TEST IS TMR THANKS

[mariamaamir]

This man literally saved me for my president calc exam on monday

[sl-]

Thank you !
This was my disaster in math before watching your video ! LOL

[mariamaamir]

great vid!! keep doing what you’re doing sir👍🏽

[chrisulfen]

Thank you so much!!!! This helped a lot!

[arnoldpino]

So only in the center region where graphs pass the horizontal? 😅

[pinkknightcreator]

How about the one in your thumbnail of the video?

[EskimoBENNY]

i have to use this for school and it actually makes 0 sense.
im bout to fail online school 2020.