Question

How do you find the asymptotes for `f( x ) = tan(x)`?

Answer 1

`tanx` has vertical asymptotes at `x=(pi/2)+npi`

Explanation:

Determine the values of `x` for which `tanx` doesn't exist.

Recall that `tanx=sinx/cosx.` If `cosx=0, tanx` does not exist due to division by zero.

We know `cosx=0` for `x=(pi/2)+npi` where `n` is any integer.

Therefore, `tanx` has vertical asymptotes at `x=(pi/2)+npi`.

No horizontal asymptotes exist for the tangent function, as it increases and decreases without bound between the vertical asymptotes.