How do you identify all asymptotes for #f(x)=-(x+2)/(x+4)#?

1 Answer
Jul 17, 2017

Answer:

#"vertical asymptote at " x=-4#
#"horizontal asymptote at " y=-1#

Explanation:

The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be and if the numerator is non-zero for this value then it is a vertical asymptote.

#"solve " x+4=0rArrx=-4" is the asymptote"#

#"horizontal asymptotes occur as"#

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

#"divide terms on numerator/denominator by x"#

#f(x)=-(x/x+2/x)/(x/x+4/x)=-(1+2/x)/(1+4/x)#

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

#rArry=-1" is the asymptote"#
graph{-(x+2)/(x+4) [-10, 10, -5, 5]}