Definition:Independent Variable/Real Function

Definition
Let $f: \R \to \R$ be a (real) function.

Let $f \left({x}\right) = y$.

Then $x$ is referred to as an independent variable.

Also see

 * Definition:Dependent 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 $x$.