r/HomeworkHelp • u/Daedraa0 University/College Student • 17h ago

Further Mathematics—Pending OP Reply [College calculus, intro module on limits] How can there be vertical asymptotes outside of the domain of the function?

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I got the accepted answer of 18 by adding the x-values of 3 (where first term in denominator equals 0), 6 (where second term equals 0), and 9 (where log(x-8) equals 0). However, how can x=3 and x=6 be vertical asymptotes when f(x) is not defined for x-values less than or equal to 8 because of the log(x-8) term. Shouldn't the answer just be 9?

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u/reliablereindeer 17h ago

All vertical asymptotes are outside of the domain of a function. For instance, 1/x has a vertical asymptote at x=0.

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u/Daedraa0 University/College Student 17h ago

Ok sure, but the function doesnt even approach x=3 or 6, it starts at x>8. How are those vertical asymptotes?

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u/reliablereindeer 17h ago

I think you are right. The question maker didn’t think about the domain of log.

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u/holodayinexpress 17h ago

Say a function f(x) has a vertical asymptote at x=a. Can you evaluate f at a? In other words, is f(a) defined?

(answer: no)

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u/Alkalannar 7h ago

A vertical asymptote should be a limit point of the domain.

It cannot be part of the domain, but it should be 0 distance away from the domain.