Question

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

Answer 1

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(x)=(x^2-3)/(x-4)`

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

hope that helped