How can you know if there's a hole, a vertical asymptote, and a horizontal asymptote in a rational function.

Question

firejay5 · Answer

What I am asking is how do you figure it out.

hero · Answer

One of the best resources on this is purplemath.com

jennychan12 · Answer

vertical asymoptote --> set denominator = zero
horizonal ---> set numerator = 0
hole ---> when the denominator is zero

firejay5 · Answer

I need it summarized based on what you know

hero · Answer

I think @jennychan12 has something to contribute that may be useful for you.

firejay5 · Answer

it seems complicated, give an example problem

jennychan12 · Answer

given y = (x-1)/(x-2)
vertical asymoptote --> set denominator = zero
horizonal ---> set numerator = 0
hole ---> when the denominator is zero

jennychan12 · Answer

denominator = bottom part
numerator = top part

hero · Answer

@Firejay5, try to think of them as three distinct cases.

firejay5 · Answer

ok

firejay5 · Answer

give a problem and work it out @Hero

hero · Answer

No disrespect bro, but I'm not your teacher.

precal · Answer

vertical asymptote is definitely taking the denominator and setting it equal to zero and solving for it; this is the number the denominator can not be

precal · Answer

|dw:1364862782996:dw|therefore x=3 is the vertical asymptote