Question

What are the vertical and horizontal asymptotes of f (x) = StartFraction 2 x Over x minus 1 EndFraction?
horizontal asymptote at y = 0, vertical asymptote at x = 1
horizontal asymptote at y = 2, vertical asymptote at x = 1
horizontal asymptote at y = 1, vertical asymptote at x = 0
horizontal asymptote at y = 1, vertical asymptote at x = 2

Answer 1

horizontal asymptote at y = 2, vertical asymptote at x = 1

Reason: denominator 0 at x = 1 gives a vertical asymptote. Degrees of numerator and denominator are equal, so the horizontal asymptote is the ratio of leading coefficients, 2/1 = 2.