Ex: Find the Intercepts, Asymptotes, and Hole of a Rational Function

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This video explains how to determine the x-intercepts, y-intercepts, vertical asymptotes, and horizontal asymptote and the hole of a rational function.

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I wish I had you as a teacher. Your voice is clear and you don't waste time.

SlappedRat

In your final slides, the Vertical Asymptote of the graph (x= -3 [~4:52]) does not reflect the Vertical asymptote of the work displayed (x= -2 [~4:30]).

gregcollins

throw on some lofi in the backround of this and it really makes this 100% better

aarongallagher

I tried this rational function: f(x) = (x^2+4x+4)/(x^2-4). I understand that if a factor in the denominator is also in the numerator an equal amount of times, there will be a hole at that zero. I also understand that if the factor in the denominator is also in the numerator, but more times in the numerator (greater multiplicity), there will also be a hole at that zero. Turns out this function (when using Desmos) will show an x intercept at x = -2 instead of a hole. Other functions with holes, when graphed with Desmos, will show me the coordinate of the hole as example: (5, undefined). For the function mentioned above, it shows the coordinate (-2, 0) as an intercept and actually crosses the x axis. I do the sign analysis before I graph and this intercept is not considered because it's a hole. I have told my students that we only consider x intercepts and vertical asymptotes for the sign analysis. Should I consider this as an intercept in the sign analysis even though it's a hole? Thank you for any input you may have.

mrstorresmath

This video helped me _so much_, I could not thank you enough.

mythics

WHERE'S THE END OF VIDEO QUOTE MATH MAN?!

keepinpemdazaliv

He was saying numerator and denominator guys, l know it didn't sound like 4 syllables each but l guess it was 😂

adairmorgan

i wish my math teacher lived in my room

kalen_cha

thank you! this video was very helpful!

daradesai

3:21 "notice that we did not use the simplified function..." He most certainly did use the simplified function folks. Just wanna put that out there.

connormasadas

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