Question

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

Answer 1

`"vertical asymptote at "x=4`
`"horizontal asymptote at "y=1`

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 "x-4=0rArrx=4" is the asymptote"`

`"horizontal asymptotes occur as"`

`lim_(xto+-oo),ytoc" ( a constant)"`

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

`y=(x/x+2/x)/(x/x-4/x)=(1+2/x)/(1-4/x)`

`"as "xto+-oo,yto(1+0)/(1-0)`

`rArry=1" is the asymptote"`
graph{(x+2)/(x-4) [-20, 20, -10, 10]}