Problem #PRU-107864

Problems Calculus Real numbers Integer and fractional parts. Archimedean property Methods Pigeonhole principle Pigeonhole principle (angles and lengths)
 13–15  3.0

Problem

A continuous function f has the following properties:

1. f is defined on the entire number line;

2. f at each point has a derivative (and thus the graph of f at each point has a unique tangent);

3. the graph of the function f does not contain points for which one of the coordinates is rational and the other is irrational.

Does it follow that the graph of f is a straight line?