How to find the vertical asymptotes and holes of a rational function (precalculus)
This precalculus tutorial covers finding the vertical asymptotes of a rational function and finding the holes of a rational function. We first set the denominator equal to 0 in order to find the candidates for the vertical asymptotes and the holes. Remember, "nonzero/0" gives you a vertical asymptote, and "0/0 from the original and no nonzero/0 from the reduced" gives you a hole.
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#precalculus
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5:41 0/0 but still gives you a vertical asymptote
Пікірлер: 18
What a master of exchanging markers....😮
Thank you king!!! Helping me pass my college algebra class !!!
OMG NOW EVERYTHING IS SEEMS EAZIER THANK YOU ❤
First, I factored the denominator to find the poles of this function. I got x = -1 and x = 4. Then, I factored the numerator to see if it shared any zeros with the denominator. I found that both the top and bottom were 0 at x = -1. So I did zero-pole cancellation, and plugged -1 into the cancelled function to see if it approached a finite value. I found that the function had a hole at (-1,0.4). So the function has a vertical asymptote at x = 4, and a hole at x = -1
2 words sum this up.....removable discontinuity
@Ninja20704
Жыл бұрын
Yeah that’s the more official name
@omargoodman2999
Жыл бұрын
Right, but this demonstrates *why,* not what. It's one thing to just say, "this is what it is, this is how to do it, just memorize the process". But by demonstrating the difference, how with one type the equation *would be* continuous if not for the discontinuity, but with the other it's an automatic V.A. in *in spite of* that one exclusion, you understand the reasoning behind the method.
The easier way to explain hole at x=a is if direct substitution creates 0/0 and the limit as x->a is finite. If the limit is infinite it becomes an asymptote regardless of the numerator being zero or not.
yo thank you for this
Thanks!! I was looking for solution when both sides of equation can't be zero. I know this one original is L'Hôpital way
well now I know why there's a hole. 0/0
Somehow I find L'Hôpital way more straightforward than factoring and reduction 😅
@solidpixel
Жыл бұрын
you do realize you are watching a *PRECALCULUS* tutorial right?
@nyandyn
Жыл бұрын
@@solidpixel Yes. I was pointing out that sometimes the more advanced tools you haven't learnt yet are more convenient.
How does he factor it so fast?
@daniaalsadi7208
11 ай бұрын
If you practice anything you will ace it and it will be just easy
@ethanmatthewapostol881
9 ай бұрын
you first need to find what makes a number into that from multiplication so like, x^2-x+12 right? then what makes a 12 is 3x4, so it makes sense because if you minus 3-4, you get -1 but in this case, -x. I don't know if I got that correctly nor used the right equation, that's how I was taught
Anything divided into 0 is undefined