Can any function represent something in the real world?

Question

We know that the volume of a cube can be represented by the function: $V(x)=x^3$, where $x$ is side length. $x^2$ can represent the volume of some material that has a constant side ($1$). The function $(x-1)(x+2)$ can represent an area that depends only on $x$. You get the point.

So my question is:

Can any algebraic or transcendental function (or combination) be the mathematical model that describes some process in the real world?

For example, the function $x^2$ describes the behavior of an area as a function of $x$.

What does a more complex function like this describes: $\displaystyle\frac{x-1}{(x+2)(x^2+4)}$ ?

We often do: real process $\to$ formulate equation that describes it. But can we do it the other way around?

EDIT:

As pointed out in the comments, maybe this question describes better what I mean:

Can all functions be used to create a mathematical model that describes something that we consider 'not mathematical'?

Answer 1

Functions in the modern sense of the word are much more general than the expressions that you seem to think of as "functions". In particular, most functions (in the sense of cardinality) cannot be specified in a finite number of symbols in a given language, and therefore would not be able to represent anything you could name, whether in the real world or out of it.

Answer 2

It's difficult to say what you mean by the existence of a real world application to each function. Certainly, there could be a very contrived application, but I think you would be hard pressed to find a natural application to some of these functions that mathematicians find useful.

The Dirichlet function: $$f(x)=\cases{0 & \text{ if $x$ is irrational}\\ 1 & \text{ if $x$ is rational.}}$$

Thomae's function: $$f(x)=\cases{0 & \text{ if $x$ is irrational}\\ \frac{1}{q} & \text{ if $x=\frac{p}{q}$ where $p$ and $q$ are relatively prime integers.}}$$

Weierstrass function: a continuous function which cannot be said to have a slope at any point (it is nowhere differentiable).

Peano curve: any parametric function $f:\mathbb R\to\mathbb R^n$ which is surjective (i.e., it covers every point in $\mathbb R^n$).