This is my first time using Mathematics SE (I've only used Physics and Astronomy before), so I apologize if this question is awkwardly phrased or incorrectly presented. I welcome any and all edits and suggestions that can make it clearer.
I'm a beginner when it comes to manifolds, and I'm just learning about transition functions. I've been working in Cartesian coordinates, in the Euclidean plane. I have a pair of differentiable functions $f(x)$ and $g(x)$ on two Cartesian coordinate charts, and I want to find a basic transition function between them. Let's say that $f(x) = 6x^2 + 2$ and $g(x) = 2x^4$. They are defined on separate coordinate charts, which are separated by a translation and a rotation. Is it possible to find a simple transition function between the two charts (possibly independent of the functions)?