Graph Rational Functions with Asymptotes, Intercepts, and Holes

In this video we go through 5 examples showing you how to graph rational functions by finding the domain, any holes (removable discontinuities), x and y intercepts, vertical asymptotes, horizontal or slant asymptotes, how to find additional points and use sign analysis to get a good sketch of your graph.
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So real

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[@MariosMathTutoring]

You’re welcome!

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[@MariosMathTutoring]

Glad it was helpful!

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[@MariosMathTutoring]

Glad it helped! Good luck on your test!

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[@MariosMathTutoring]

Glad it was helpful!

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Glad my videos are helping you!

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[@MariosMathTutoring]

Glad it was helpful!

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[@MariosMathTutoring]

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[@MariosMathTutoring]

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[@MariosMathTutoring]

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[@MariosMathTutoring]

No, sorry

[@daisy9537]

This was really helpful, thank you so much. I just have one question, can the graph touch or cross the slant asymptote?

[@MariosMathTutoring]

Yes, absolutely

[@daisy9537]

@@MariosMathTutoring but aren't asymptotes supposed to be parts where the graph never touches but gets close to

[@Panicnow2207]

@@daisy9537 I know this response is late, but just in case others are wondering about the same thing. The VA asymptote is never crossed. The other asymptotes can intersected since they are about the end behavior of the graph. so if y=0 is an asymptote, then as x approached pos or neg infinity, the y value appraoches 0. However, the function could be 0 for mid values of x. try y=x/(x^2+1)

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