Question

How to find the asymptotes of `y=22/(x+13)-10`?

Answer 1

`"vertical asymptote at "x=-13`
`"horizontal asymptote at "y=-10`

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+13=0rArrx=-13" is the asymptote"`

Horizontal asymptotes occur as

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

divide terms on numerator/denominator by x

`y=(22/x)/(x/x+13/x)-10=(22/x)/(1+13/x)-10`

as `xto+-oo,yto0/(1+0)-10`

`rArry=-10" is the asymptote"`
graph{((22)/(x+13))-10 [-40, 40, -20, 20]}