Question

How do you identify all asymptotes for `f(x)=1/(x-1)`?

Answer 1

vertical asymptote at x = 1
horizontal asymptote at y = 0

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 vertical asymptote.

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

Horizontal asymptotes occur as

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

divide terms on numerator/denominator by x

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

as `xto+-oo,f(x)to0/(1-0)`

`rArry=0" is the asymptote"`
graph{1/(x-1) [-10, 10, -5, 5]}