How do you find the vertical, horizontal or slant asymptotes for #y=(13*x)/(x+34)#?

1 Answer
Aug 27, 2017

Answer:

#"vertical asymptote at "x=-34#
#"horizontal asymptote at "y=13#

Explanation:

The denominator 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+34=0rArrx=-34" is the asymptote"#

#"horizontal asymptotes occur as "#

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

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

#y=((13x)/x)/(x/x+(34)/x)=13/(1+34/x)#

as #xto+-oo,yto13/(1+0)#

#rArry=13" is the asymptote"#

Slant asymptotes occur when the degree of the numerator > degree of the denominator. This is not the case here hence there are no slant asymptotes.
graph{(13x)/(x+34) [-80, 80, -40, 40]}