How to find the asymptotes of #y=22/(x+13)-10#?

1 Answer
Mar 2, 2017

Answer:

#"vertical asymptote at "x=-13#
#"horizontal asymptote at "y=-10#

Explanation:

The denominator of y cannot be zero as this would make y 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+13=0rArrx=-13" is the asymptote"#

Horizontal asymptotes occur as

#lim_(xto+-oo),ytoc" ( a constant)"#

divide terms on numerator/denominator by x

#y=(22/x)/(x/x+13/x)-10=(22/x)/(1+13/x)-10#

as #xto+-oo,yto0/(1+0)-10#

#rArry=-10" is the asymptote"#
graph{((22)/(x+13))-10 [-40, 40, -20, 20]}