Question

What are the asymptotes of `f(x) = (2x-1) / (x - 2)`?

Answer 1

`"vertical asymptote at "x=2`
`"horizontal 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)`

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