Question

Please help! Which function does not have a vertical asymptote?
A. y=5x/1-x^2
B. y=x/1+x^2
C. y=5x-1/x
D. y=5x/x+x^2

Answer 1

Do you know what is a vertical asymptote is?

Answer 2

HINT:
a vertical asymptote occurs when x cannot equal to something.

Answer 3

@ali1029, so what do you think?

Answer 4

i am so sorry @SolomonZelman, I had to help my little brother with something. I got your message but can you please explain to me how you got that answer?

Answer 5

I gave you a hint above....

Answer 6

well yes, i saw that but what steps did you take to find the answer? did you just put a 0 in for all of the x's?

Answer 7

it says that the answer is B.

Answer 8

Yup!
and in choices x is either 1 or 0, but in a x could be anything.

Answer 9

... (_^^)
All these choices have denominators which are functions of x, right?

Answer 10

I mean a is the answer.

Answer 11

And you already said y.

Answer 12

The answer is B though :)

Answer 13

I know it is. I really though it's A, sorry!

Answer 14

Look @ali1029 all these choices have their denominators, aye?
So... there's something special about the denominator in choice B... do you know what it is?

Answer 15

it's okay @SolomonZelman . & no, I'm not too sure what makes the denominator special :o @terenzreignz

Answer 16

It's simple ^_^
The denominator in B could NEVER be equal to zero, no matter what value x takes.
1+x^2
1 is positive, and x^2 is always positive (or zero)
either way, the denominator in choice B is always going to be at least 1.
Does that make sense?

Answer 17

Look at choice A.
1 - x^2
it becomes zero when x = 1 or x = -1

Look at choice C
x
clearly, this is zero when, well, x = 0
LOL


Look at choice D
x+x^2
This is zero when x = 0 or x = -1


but choice B, no matter what value x takes, 1+x^2 is never zero, and a vertical asymptote is something that results from a zero-denominator ^_^

Answer 18

Ohh, i see, that completely makes sense now! thank you so much :) if you dont mind, do you think you could help me with a few more problems i have on this topic? i really need to make a good grade :o

Answer 19

Maybe one more. I'm sleepy ^_^

Answer 20

oh haha i just woke up :p

Answer 21

well, what would the horizontal asymptote be for the function: y=x^2/x^2-9?

Answer 22

oh, lol, is this a calculus question?

Answer 23

i think so, im in pre calculus :o

Answer 24

Can we use limits?

Answer 25

i'm not sure, i dont really know what those are lol, heres the official question

Answer 26

Well, I'll give you a shortcut then, but this only works if the highest powers in both the numerator and denominator are equal, ok?

In this case, in the numerator, the highest power is 2, same in the denominator, right?

Answer 27

correct!

Answer 28

Then, the asymptote at infinity would simply be the quotient of their coefficients, both of which are 1, s....?

Answer 29

so the horizontal asymptote would just be 1?

Answer 30

Yup.

Answer 31

Well... I'm signing off now...
Good luck with your grade :)
--------------------------------
Terence out

Answer 32

Thank you so much, you're amazing! :)

Answer 33

he taught me the limits, or almost did....

Answer 34

haha yep :p