How do you find the asymptotes for #r(x) = (-1) / (x +1)^2#?

1 Answer
Jim G.
Jul 22, 2018

#"vertical asymptote at "x=-1#
#"horizontal asymptote at "y=0#

Explanation:

The denominator of r(x) cannot be zero as this would make r(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+1)^2=0rArrx+1=0#

#x=-1" is the asymptote"#

#"Horizontal asymptotes occur as"#

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

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

#r(x)=-(1/x^2)/(x^2/x^2+(2x)/x^2+1/x^2)=-(1/x^2)/(1+2/x+1/x^2)#

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

#y=0" is the asymptote"#
graph{-1/(x+1)^2 [-10, 10, -5, 5]}

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