Question

How do you find the vertical, horizontal or slant asymptotes for `f(x) = 3(1/x)`?

Answer 1

Asymptotes: y = 0 and x = 0.

Explanation:

x y = `c^2` represents a rectangular hyperbola .
The axis is y = x.
the asymptotes are the axes of coordinates.
The two branches are in the 1st and 3rd quadrants.
Here, c = `sqrt3`
Vertices are `(sqrt3, sqrt3) and (-sqrt3, -sqrt3)`
The eccentricity of a rectangular hyperbola is `sqrt2`.
The foci are `(sqrt6, sqrt6) and(-sqrt6, -sqrt6)`(