Find the vertical horizontal and oblique asymptotes if any o

Find the vertical, horizontal, and oblique asymptotes, if any, of this rational function. R(x) = 2x + 4/x - 6 Find the vertical asymptote. (If there is not one enter NONE.) Find the horizontal asymptote. (If there is not one enter NONE.) Find the oblique asymptote. (If there is not one enter NONE.)

Solution

R(x) = (2x +4)/(x - 6)

Vertical aymptote ==> denominator = 0

==> x - 6 = 0

==> x = 6

Hence equation of vertical asymptote is x = 6

Horizontal asymptote ==> y = (leading coefficient of numerator)/(leading coefficient of denominator)

==> y = 2/1

==> y = 2 is equation of Horizontal asymptote

Oblique asymptotes : None (since the degree of numerator and degree of denominator are equal)