# How do you find the asymptotes for #g(x) = (2x^2 - 8x) / (x^2 - 6x + 8)#?

##### 1 Answer

#### Explanation:

Start by factorizing the numerator and denominator to obtain

Since we cannot divide by zero as it is undefined, the function may not have inputs that lead to division by zero.

Hence

Since the other factor cancelled out, it implies that

There are no even square roots to consider so no more vertical asymptotes.

Now to find horizontal asymptotes, we investigate the limit of the function at positive and negative infinity :

Hence

The graph of the function verifies this :

graph{(2x^2-8x)/(x^2-6x+8) [-14.33, 17.71, -6.43, 9.59]}