Find the horizontal and vertical asymptotes of the curve.

Question

Find the horizontal and vertical asymptotes of the curve.

y = x2 − x

x2 − 6x + 5

 

x	=
y	=

Answer 1

Assuming that this is (x^2 - x)/(x^2-6x+5) = (x-1)(x)/((x-1)(x-5)), we have

a vertical asyptote at x = 5 (there is an x - 5 in the denominator), a hole at x = 1(x-1 in the numerator and denominator), and a horizontal asymptote at y = 1 (second degree polynomial in the numerator and denominator with leading coefficient of 1 in both cases implies limit of 1/1 = 1).