Question

Find all vertical asymptotes of the following function.

Answer 1

\(\Large f(x) = \frac{\sqrt{x - 3}\sqrt{x^2 + 4}}{(x+4)(x-3)(x-5)}\)

Answer 2

So the domain is restricted to x > 3 because of sqrt(x - 3)

So that means x = -4 cannot be a vertical asymptote.

x = 5 is a vertical asymptote

My question is, does x = 3 count as a vertical asymptote?

Answer 3

I believe it does but since the domain is restricted to x > 3 I'm not so sure :b

Answer 4

@mathmale

Answer 5

@pooja195 @procrastilate

Answer 6

Thank you for tagging others, giitter but there is no need to. I haven't tagged anyone because I have time and I don't want to bother people to help me. If the users want to help, they'll see my post and come and help. Just because they have a high SS doesn't mean they necessarily know the answer or want to help at the moment.

Answer 7

have you tried graphing the function?

Answer 8

You are right as to x=5 being an asymptote, and if the domain is strictly x>3 then x=3 cannot be an asymptote since 3 is not greater than 3.

Answer 9

wait a bit

Answer 10

x=3 will be a vertical asymptote

Answer 11

because lim x tends to 3+ f(x), check the limit

Answer 12

the denominator will be then sqrt(x-3) and hence x=3 will be a vertical aysmtote

Answer 13

@TheSmartOne

Answer 14

^ yea I think i am wrong then.

Answer 15

Check the definition, in any book, its given as x tends to a+ or a-, it never checks at x=a. , since the aymptote will never converge with the original function

Answer 16

Yes, x = 3 and x = 5 are both vertical asymptotes.

Thanks! :)

A definition that was given in class by the TA was if h(x) = f(x)/g(x)

there will be a vertical asymptote when x = c for when g(c) = 0 but f(c) cannot equal to 0 also