Definition:Independent Variable/Real Function
Let $f: \R \to \R$ be a real function.
Let $\map f x = y$.
Then $x$ is referred to as an independent variable.
The terms independent variable and dependent variable arise from the idea that it is usual to consider that $x$ can be chosen independently of $y$, but having chosen $x$, the value of $y$ then depends on the value of $x$.