Find the asymptotes for p(x)=-4x-1/x-5
Find the asymptotes for p(x) = (-4x-1)/(x-5)
The denominator, (x-5), equals zero at x=5. So there will be a
vertical asymptote at x=5.
When the degree of the numerator and denominator are the same, there will be a horizontal asymptote that is equal to the ratio of the coefficients of the highest degree terms. The "degree" refers to the highest exponent. In this case, it's x^{1}, or just x, in both the numerator and the denominator. The coefficient of the x term in the numerator is -4, and in the denominator it's 1. The
horizontal asymptote, then, is y = (-4)/1 = -4.