How do you identify the horizontal asymptote for #2/(x+3)#?
1 Answer
Explanation:
Without using any calculus concepts, such as the limit, here are the general rules for the horizontal asymptotes of a rational function in the form of

If the degree of the numerator is less than the degree of the denominator,
#y=0# is the horizontal asymptote. 
If the degree of the numerator is greater than the degree of the denominator, we have no horizontal asymptote, but rather a slant asymptote.

If the degree of the numerator and the degree of the denominator are equal, the horizontal asymptote is
#y=a/b# where#a# is the coefficient of the term of highest degree in the numerator and#b# is the coefficient of the term of highest degree in the denominator.
We have case 1 here (the degree of the numerator is
With limits:
Take
Therefore,