When people refer to the "$x$-dimensional" case of a function or relation, how is the dimensionality determined?
For example, let's say I have the functions $f(x,t)$ and $g(x, t)$.
I could refer to them as being three dimensional, because each function has three variables ($x$, $t$, and the output) and therefore must be graphed on a 3-D plane.
I could also refer to each function as two dimensional. This is because for every point, only the two inputs have to be known to determine the position on the graph. (Or equivalently, the graph can be collapsed into a flat 2-D plane)
If I wanted to plot both functions on the same object, I could call it as four-dimensional. It has two inputs and two outputs, needing to be graphed in 4-space. (Like a complex function)
Or even, since $t$ is a variable of time and $x$ seems to be the only variable of space, I could refer to it as taking place in one dimension, plus time. This seems to be the convention in physics-based problems like the wave and heat equations.
What is the most accepted convention for an arbitrary function or relation, and how can I best avoid confusion?