Question

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

Answer 1

vertical asymptote x = 4
horizontal asymptote y = -1

Explanation:

The denominator of f(x) cannot be zero as this would be 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 = 0 → x = 4 is the asymptote

Horizontal asymptotes occur as

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

divide terms on numerator/denominator by x

`(-x/x)/(x/x-4/x)=(-1)/(1-4/x)`

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

`rArry=-1" is the asymptote"`
graph{(-x)/(x-4) [-10, 10, -5, 5]}