How do you find the asymptotes for #f(x) = sqrt(x^2+5) - x#?

1 Answer
Feb 6, 2017

Answer:

Horizontal asymptote : #y = 0 larr# See illustrative graph.

Explanation:

#f = sqrt(x^2+5)-x =( (sqrt(x^2+5)-x)( sqrt(x^2+5)+x))/ (sqrt(x^2+5)+x)#

#=(x^2+5-x^2)/ (sqrt(x^2+5)-x)+5/( sqrt(x^2+5)+x)#

#to 0#, as #x to oo#

So, y = 0 is the asymptote, .

graph{(sqrt(x^2+5)-x-y)y=0 [-10, 10, -5, 5]}