Can every continuous function that is curved be expressed as a formula? By "curved", I mean that there is no portion of a graph of a function that is a straight line. (Let us first limit the case into 2-dimensional cases.. and if anyone can explain the cases in more than 2-dimensional scenarios I would appreciate.. but what I really want to know is the 2-dimensional case.)
Let us also say that a function is surjective (domain-range relationship).
So, can every continuous and curved function be described as a formula, such as sines, cosines, combinations of them, or whatever formula?
thanks.

The answer depends a little on what you consider a formula. The function $f(x)=-x^2$ for $x<0$, $f(x)=x^3$ for $x\ge 0$ is nicely curvy, and continuous everywhere.  The function is also surjective, and injective. 
