How do you find the vertical, horizontal and slant asymptotes of: #y= (x+2)/(x^2-64)#?
1 Answer
Jun 22, 2018
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.
