Question

What are the equations of the asymptotes of the graph of the function f (x) = StartFraction 3 x squared minus 2 x minus 1 Over x squared + 3 x minus 10 EndFraction?
x = –5, x = 2 and y = 3
x = –2, x = 5 and y = 3
x = 3, y = –5, and y = 2
x = 3, y = –2, and y = 5

Answer 1

x = –5, x = 2 and y = 3.

Reason: x^2+3x−10 = (x+5)(x−2) so vertical asymptotes at x = −5 and x = 2 (numerator ≠ 0 there). Degrees are equal, so horizontal asymptote y = ratio of leading coefficients = 3/1 = 3.