Question

How do you find the asymptotes for `R(X)= (3x+5)/(x-6)`?

Answer 1

vertical asymptote at x = 6
horizontal asymptote at y = 3

Explanation:

The denominator of R(x) cannot be zero as this would make R(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-6=0rArrx=6" is the asymptote"`

Horizontal asymptotes occur as

`lim_(xto+-oo),R(x)toc" (a constant)"`

divide terms on numerator/denominator by x

`((3x)/x+5/x)/(x/x-6/x)=(3+5/x)/(1-6/x)`

as `xto+-oo,R(x)to(3+0)/(1-0)`

`rArry=3" is the asymptote"`
graph{(3x+5)/(x-6) [-20, 20, -10, 10]}