How do you find the vertical, horizontal or slant asymptotes for #f(x) = (2x-1) / (x - 2)#?

1 Answer
Jun 12, 2018

Answer:

#"vertical asymptote at "x=2#
#"vertical asymptote at "y=2#

Explanation:

The denominator of f(x) cannot be zero as this would make f(x) 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-2=0rArrx=2" is the asymptote"#

#"horizontal asymptotes occur as"#

#lim_(xto+-oo),f(x)toc" ( a constant)"#

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

#f(x)=((2x)/x-1/x)/(x/x-2/x)=(2-1/x)/(1-2/x)#

#"as "xto+-oo,f(x)to(2-0)/(1-0)#

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