How do you find the asymptotes for #y= (x + 1 )/( 2x - 4)#?

1 Answer
Jul 6, 2017

Answer:

#"vertical asymptote at " x=2#
#"horizontal asymptote at " y=1/2#

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 " 2x-4=0rArrx=2" is the asymptote"#

#"horizontal asymptotes occur as "#

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

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

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

as #xto+-oo,yto(1+0)/(2-0)#

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