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 x1, 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.