Question

How do you find the vertex for the function `f(x)=1/x`?

Answer 1

This hyperbola can be written `xy=1`, which is symmetric in `x` and `y`, so the vertices must lie on the line `y = x`, that is at `(1, 1)` and `(-1, -1)`

Explanation:

The line `y = x` intersects `y = 1/x` at the points `(-1, -1)` and `(1, 1)`, where both equations are satisfied.

graph{(y-x)(xy-1) = 0 [-10, 10, -5, 5]}