Is There A Function Of Constant Area? If I take a point $(x,y)$ and multiply the coordinates $x\times y$ to find the area $(A)$ defined by the rectangle formed with the axes, then is there a function $f(x)$ so that $xy = A$, regardless of what value of $x$ is chosen? 

Take any desired real value $A$, then from $xy = A$, define $$f: \mathbb R\setminus \{0\} \to \mathbb R,\quad f(x) = y = \dfrac Ax$$ 
