Question

How would I know if a given equation has a vertical asymptote or not?

Answer 1

Like, I know how to solve it (hopefully), but I'm not sure if I'd be able to identify an equation that doesn't have a vertical asymptote or if it does. I'd just assume they all do.

Answer 2

If you have an equation in the form

f(x)/g(x) you will have a vertical asymptote whenever g(x) = 0

*sorry, on my phone so I can't make it look nicer than that lol

Answer 3

That's totally fine. And okay, so as long as it's a fraction in which the denominator does not equal 0?

Answer 4

Exactly

Now that's not to say it won't ALWAYS be a fraction right off the bat

Think about trig functions

tan(x) specifically

If I asked you to find the vertical asymptotes, what would you say?

Answer 5

It'd be hard because you don't see it as a fraction right away

But if you then remember

Tan(x) = sin(x)/cos(x)

You can then find where cos(x) = 0 and those would be your vertical asymptotes

Answer 6

But for just general equations, yes, whenever you have a fraction and the denominator can not equal 0 then you will not have any vertical asymptotes

Answer 7

Ah yes! I'll keep that in mind since I might see it in the future. Thank you so much!

Answer 8

Not a problem!