Choice of the point one on the top of the function if the number of points is odd

Given a function f. This function could be a sin, cos, Dirac or triangle functions. I need to find a number of points in this function.

Example: Let f is a triangle function and define 3 points ( random) as shown in the picture.

1. How to define randomly three points: one on the top, one on the left side and one on the right side?