What are the asymptotes of #f(x) = (2x-1) / (x - 2)#?
1 Answer
Jan 23, 2018
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)#
#rArry=2" is the asymptote"#
graph{(2x-1)/(x-2) [-10, 10, -5, 5]}