Question

What are the asymptotes of `f(x)=(1-5x)/(1+2x)`?

Answer 1

`"vertical asymptote at "x=-1/2`
`"horizontal asymptote at "y=-5/2`

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 verical asymptote.

`"solve "1+2x=0rArrx=-1/2" is the asymptote"`

`"horizontal asymptotes occur as"`

`lim_(xto+-oo),f(x)to c" ( a constant)"`

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

`f(x)=(1/x-(5x)/x)/(1/x+(2x)/x)=(1/x-5)/(1/x+2)`

as `xto+-oo,f(x)to(0-5)/(0+2)`

`rArry=-5/2" is the asymptote"`