What are the asymptotes of f(x) = (2x-1) / (x - 2)f(x)=2x−1x−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"solve x−2=0⇒x=2 is the asymptote
"horizontal asymptotes occur as"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]}
