How do you find the asymptotes for # f(x)=(3x)/(x-8)#?
For the horizontal asymptote, we want to compare the degrees of the numerator and denominator.
Comparing the degrees, we have
We can cancel the variables to be left with a horizontal asymptote at
To think about the vertical asymptote, we want to think about what value makes our function undefined.
In our case, this function will be undefined when the denominator is equal to zero, and we see this happens at
With this in mind, we can say we have a vertical asymptote at
Hope this helps!