How do you find the vertical, horizontal and slant asymptotes of: #y= (x+2)/(x^2-64)#?

1 Answer
Jun 22, 2018

Answer:

vertical asymptote = 8 and -8
horizontal asymptote = 0
slant asymptote = does not exist

Explanation:

  • To work out the vertical asymptote we let the denominator = 0 and solve for x
    #x^2-64=0#
    #x^2=64#
    #x=+-sqrt64#
    #x=8, x=-8#

  • For the horizontal asymptote, since the degree of the denominator is greater than the degree of the numerator- that is, #x^2>x#, the horizontal asymptote is simply y = 0

  • Lastly, to work out the slant asymptote, since the degree of the numerator is not greater than the degree of the denominator ( #x < x^2#) there is no slant asymptote.