How do you find the Vertical, Horizontal, and Oblique Asymptote given #f(x) = ((x – 10)(x + 5) )/( (13x + 10)(10–x))#?
The vertical asymptote is
First notice that
(Since that factor reduces out we know that the function has a removable discontinuity--or hole--at x = 10, but that wasn't asked.)
Horizontal asymptotes are the ratio of the leading coefficients of the numerator and denominator if both the numerator and denominator have the same degree (which they do in this case).
The horizontal asymptote in this case is