How do you find the horizontal asymptote for #g(x)=(x+3)/(x(x+4))#?

1 Answer
Mar 22, 2018

Answer:

#y=0#

Explanation:

#"horizontal asymptotes occur as"#

#lim_(xto+-oo)g(x)toc" (a constant)"#

#"divide terms on numerator/denominator by the highest"#
#"power of x, that is "x^2#

#g(x)=(x/x^2+3/x^2)/(x^2/x^2+(4x)/x^2)=(1/x+3/x^2)/(1+4/x)#

#"as "xto+-oo,g(x)to(0+0)/(1+0)#

#rArry=0" is the asymptote"#
graph{(x+3)/(x^2+4x) [-10, 10, -5, 5]}