How do you find the Vertical, Horizontal, and Oblique Asymptote given #y= (x + 1) / (2x - 4)#?

1 Answer
Aug 7, 2016

Answer:

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

Explanation:

The denominator of y cannot be zero as this is 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

#(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"#

Oblique asymptotes occur when the degree of the numerator > degree of the denominator. This is not the case here (both of degree 1) Hence there are no oblique asymptotes.
graph{(x+1)/(2x-4) [-10, 10, -5, 5]}