How do you find the vertical, horizontal or slant asymptotes for #(x+2) /( x-1)#?
1 Answer
vertical asymptote x = 1
horizontal asymptote y = 1
Explanation:
Vertical asymptotes occur as the denominator of a rational function tends to zero. To find the equation let the denominator equal zero.
solve : x - 1 = 0 → x = 1 is the asymptote
Horizontal asymptotes occur as
#lim_(x→±∞) f(x) → 0# divide numerator / denominator by x
# (x/x +2/x )/(x/x - 1/x) = (1 + 2/x)/(1 - 1/x)# as
#x ->oo " both " 2/x" and " 1/x → 0 # hence asymptote is y = 1
Here is the graph of the function
graph{(x+2)/(x-1) [-10, 10, -5, 5]}
