Question

find the vertical, horizontal, and oblique asymptotes, if any, for the given rational function.

G(x)=x^4-1 over 2x^2-2x

Answer 1

G(x)=\[x^4-1 \over 2x^2-2x\]

Answer 2

no horizontal because \[\lim_{x \rightarrow \infty } G(x)= infinity\]
no oblique cause the degree of the numerator is bigger than the degree of the denominator by 2
the vertical asymptote :\[\frac{ (x+1)(x-1)(x^2+1) }{ 2x(x-1) }\] so when only x goes to zero we have a vertical asypmtote

Answer 3

lim G(x)? What is that?

with the vertical asymptote, how do I find what x is equal to?

Answer 4

we find the lim to infinity when checking the horizontal asymototes
the vertical asymptote is stated at x=something when the function goes to pm infinity at something

Answer 5

what is lim?

Answer 6

limit O_o

Answer 7

oh. and how do I go about checking the asymptotes? I know nothing about this stuff

Answer 8

I have just told you about HA and VA, the oblique exist in the rational functions when the degree of the numerator is bigger that the denominator by one most times, I think u dont need to know anything further about it

Answer 9

I don't understand algebra at all. I don't know how to solve for the HA or the VA or the oblique. I don't understand how to do any of this.

Answer 10

@Ahmad1 try using a different approach other than a calculus approach

Answer 11

I really mean no offense at all @Jewels89 , but learning about asymptotes needs a preknowledge about the limits and factoring, I don't think I am capable to tell you all that right now so I really recommend you to read about limits and to have some knowledge about factoring so well because you will need them to do this stuff..
would you mind if I asked how old are you?

Answer 12

try this it may help you understand..
http://www.khanacademy.org/math/trigonometry/polynomial_and_rational/asymptotes-graphing-rational/v/asymptotes-of-rational-functions

Answer 13

I have read about it. I've read this area over 5 times and I still don't understand it. I'm 24 years old, never have understood algebra and no one takes the time to ever really explain anything to me because it's my weakest subject.

Answer 14

thank you @Luigi0210 I really understand your good intension , but I think that what @Jewels89 should do ..

Answer 15

First, establish the HOLE at x = 1, then reduce the problem

\(g(x) = \dfrac{(x+1)(x^{2}+1)}{2x} = \dfrac{1}{2}\dfrac{x^{3} + x^{2} + x + 1}{x}\)

This suggests immediately a Vertical Asymptote at x = 0

\(g(x) = \left[\dfrac{x^{2} + x + 1}{2}\right] + \dfrac{1}{2x}\)

The part in the square brackets is your asymptote. It is quadratic. It is neither horizontal nor oblique.

Answer 16

no no that's an idea in your mind @Jewels89 ,I've learned algebra, geometry and calculus by my self not because I am smart but because I had to ....
if you have the same motivation I had I am sure you will understand it very well, and I wish I have the names of an English sites that learn these things but looks our friend @ Data_LG2 does, I wish you very gd luck

Answer 17

The problem with me, is my mind doesn't work that way. I can't take something new and learn it and this was never touch when I was in high school and junior high

Answer 18

I have to agree with @Ahmad1 When and why did you decide math was not for you and your mind didn't work that way? Give that up. Never say it or think it again. It's a lot like learning a new language. Get used to the grammar and syntax, learn some vocabulary, and you are good to go after practice, practice, and more practice.

Answer 19

when I learned the same thing 3 days in a row, but still didn't not know how to do it. I try. I honestly try, but I never know how to apply things to certain equations or what equations to apply a certain techniques or whatever. It's not just how I feel or think.

Answer 20

Don't forget to take deep breaths and get plenty of sleep and eat a balanced diet.

Answer 21

looks like @Jewels89 hasn't seen me the first year I started learning English lol , you will never learn math unless you believed it, also you have to use self-learning especially these times because you will be under pressure If you made someone teach you , then after you learn the basics try me or any other one who can help ;)