Problem 4
A point in the plane with a Cartesian coordinate system is called a mixed point if one coordinate is rational and the other is irrational. Find all polynomials with real coefficients whose graphs contain no mixed point.
Step 1 of 7: Translate the graph condition
Detailed analysis
A rational input cannot have an irrational output, and an irrational input cannot have a rational output; otherwise the graph point would be mixed.