Question

How do you find the asymptotes for `y= (x + 1 )/( 2x - 4)`?

Answer 1

`"vertical asymptote at " x=2`
`"horizontal asymptote at " y=1/2`

Explanation:

The denominator of y cannot be zero as this would make y 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"`

`y=(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"`
graph{(x+1)/(2x-4) [-10, 10, -5, 5]}