# How do you find the slant asymptote of f(x)=(x-3)/(x-4)?

Jan 13, 2016

Since the highest exponent for both the numerator and denominator is the same (it's 1), there is no slant asymptote .

#### Explanation:

You will have a slant asymptote when the greatest exponent in the numerator exceeds the greatest exponent in the denominator by 1.

For example, the following function will have a slant asymptote:

$f \left(x\right) = \frac{{x}^{2} - 3}{x - 4}$

Because the exponent $2$ exceeds $1$ by exactly 1 unit.

hope that helped