For what values of a and m does f(x) have a horizontal asymptote at y = 2 and a vertical asymptote at x = 1? f(x)=2x^m/x+a which is the answer a = –1, m = 0 a = 1, m = 0 a = –1, m = 1 a = 1, m = 1

will have a horizontal asymptote of if



where at least one of these limits needs to be satisfied. Since we would like



to converge to 0, we need the term to disappear in the numerator. The only way for that to happen is if . Then



and this does indeed approach 0 as gets arbitrarily large.

Now, in order to have a vertical asymptote at , all we need to do is set . Then



does not exist, as required.

The answer is part a: use