Test a functional equation

You will write three tests for functional equations. Each test tries a candidate function on every pair from a grid of numbers. A computer cannot prove that a function solves an equation, but it can show that a candidate fails.

The idea. For the equation $f(x + y) = f(x) + f(y)$, compute the gap $f(x + y) - f(x) - f(y)$ for many pairs. If every gap is zero, the candidate passes. The other two equations are $f(x + y) = f(x)f(y)$ and $f(xy) = f(x) + f(y)$ for positive $x$ and $y$.

Your tasks.

1. Finish is_additive(f). Return True when f(x + y) = f(x) + f(y) for every pair from VALUES, within 0.000001.
2. Finish is_multiplicative(f). Do the same for f(x + y) = f(x) * f(y).
3. Finish is_logarithmic(f). Do the same for f(x * y) = f(x) + f(y), using the numbers in POSITIVE.