There are a couple of similar questions on this site but I don't think they answer the same issue (or I don't understand the answers enough to know if they do).
I have a function which takes X,Y coordinates and does some operations, let's say it multiplies the X coordinate by 2 and adds 3, multiplies the Y coordinate by 10, then outputs the new X',Y' coordinates. I'm a programmer and I need to translate my function into an equation suitable for publication.
What is the correct notation for this? I could describe f(x) and f(y) separately, but I keep thinking there must be a notation to do both in one line? There are lots of mathematical operations that work on coordinates...
Based on your last comment, one possible way of writing your function is the following. Let $(x,y)$ denote a point in space. Because temperature and altitude are scalars, we can say that the temperature at $(x,y)$ is $T(x,y)$, and the altitude at $(x,y)$ is $A(x,y)$. Note that both $T$ and $A$ are functions that take two inputs $(x,y)$, and produce one output. Then, you can introduce a new function $F$ that also takes two inputs, but produces two outputs, i.e., $$ F(x,y) = \left(T(x,y), A(x,y) \right). $$ Basically, every time you call $F$ with the inputs $(x,y)$, internally you call $T$ and $A$ with those same inputs and return their corresponding outputs.