How do you find the vertical, horizontal or slant asymptotes for # y = 6/x#?
1 Answer
we have a vertical asymptote at
we have a horizontal asymptote at
graph{6/x [13.38, 16.53, 7.87, 7.09]}
Explanation:
Given:
Required vertical, horizontal or slanted asymptotes?
Solution Strategy: Definition and principles governing asymptotes.
Asymptotes Rule:
Let f be the (reduced) rational function

The graph of
#y = f(x)# will have vertical asymptotes at those values of#x# for which the denominator is equal to zero. 
The graph of
#y = f(x)# will have horizontal asymptote if:
a.#m > n# (the degree denominator#gt# numerator) then
#y = f(x)# will have a horizontal asymptote at y = 0 (xaxis)
b. If#m = n# (degree of numerator and denominator are the same),
then#y = f(x)# will have a horizontal asymptote at#y =a_n/b_m#
c. If#m < n# (numerator degree is larger than denominator), then the graph of y = f(x) will have no horizontal asymptote
From 1) we have a vertical asymptote at
From 2a