# How do you find the asymptotes for #f(x)= (4x^2+5)/( x^2-1)#?

##### 1 Answer

To find vertical asymptote, you must set the denominator to 0 and then solve.

#### Explanation:

This can be factored as a difference of squares

Now for horizontal asymptotes, which are a little trickier.

To find these, you must look for the highest power (exponent) in both the numerator and the denominator. The highest power in both is

So, the horizontal asymptote occurs at

Verification:

Plugging in 4 for

This proves that there is a horizontal asymptote at y = 4, because an asymptote is essentially and undefined line on the graph of a function.

**Practice exercises:**

- Identify all the asymptotes in
#g(x) = (5x^2 + 10x)/(2x^2 + 7x + 3)#

Good luck!