How do you find the asymptotes for # y= (x+2)/(x-4)#?

1 Answer
Jan 24, 2018

Answer:

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

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-4=0rArrx=4" is the asymptote"#

#"horizontal asymptotes occur as"#

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

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

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

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

#rArry=1" is the asymptote"#
graph{(x+2)/(x-4) [-20, 20, -10, 10]}