Creating a polynomial function from a few points is a fundamental task in mathematics and computer science. Given a set of points, we can construct a polynomial function that passes through all of them; this function can be used to interpolate or approximate other values within the same domain. One common method for constructing such a polynomial is Lagrange interpolation.
Lagrange interpolation works by constructing a unique polynomial of degree n-1, where n is the number of given points. The polynomial is constructed such that it takes on the value of the ith point at x = xi. This can be expressed mathematically as: