In calculus, everything is a function. We don't just define an equation, we turn it into one or more functions to work with.
For instance, instead of saying that \(y = 3x\), we would say that \(y\) is a function of \(x\); we would then write it as
\(y=f(x)\) where \(f(x)=3x\). At first, this may seem a bit daunting, but after a while, it becomes easy. The purpose for
refering to functions instead of equations becomes clear once you delve a bit deeper into the calculus. The idea of a function
replacing part of an equation is analagous to algebra substituting letters for numbers. And just like algebra, these substitutions
make the math much easier in the long run.
Especially when working with the long-hand forms of calculus, we tend to work with a lot of limits. This is because calculus deals mostly with infinitessimally small slices, and limits are the best, if not the only way to do this.