Question

Create a rational function with vertical symptote x=-2 & x=2, and horizontal asymp. y=0.
I have f(x)=g(x)/(x-2)(x+2)

I dont know what to do with a horizontal asymp. of y=0, how do you make an equation of that?>

Answer 1

Actually, would it be okay to have the denominator be (x^2-2), I believe that equals (x-2)(x+2) if my mental math is right.

Answer 2

@tanya123 Can you help?

Answer 3

recall that (x-a)(x+a) = (x²-a²). You want a horizontal asymptote at y=0: you can use any linear function or a constant (because their degrees are lower than denominator's degree). That's because when you take \(\large{lim_{ x \rightarrow ±\infty }\frac{g(x)}{f(x)}}\) you will get 0

Answer 4

@ChillOut So I could use x?

Answer 5

And yeah that would make a cubed x variable Thanks for catching that. :)

Answer 6

Yes, x is fine.

Answer 7

so; x/(x-2)(x+2) is ok for the equation?

Answer 8

For the given situation?

Answer 9

Yup. http://www.wolframalpha.com/input/?i=x%2F%28%28x%2B2%29%28x-2%29%29

Answer 10

Check the plot :)

Answer 11

OK. I thought so from the beginning but wan't all that sure. Thank you so very much :)