Function of one variable

Definition: A function of the variable $x$ is a prescription $y(x)$, which calculates a number, the function value, for any feasible value of the variable $x$.

The set of all feasible values $D$ of $x$ is called the domain of the function.


Remark: The function values $y(x)$ can be interpreted as the values of a variable. If we call this variable $y$, then $y$ and $x$ satisfy the equation
$$\begin{align} y & =y(x). \end{align}$$
The variable $x$ in $y(x)$ is called the independent or input variable and the variable $y$ is called the dependent or output variable.


Example: A function of the variable $t$ is for instance $N(t)=2t+3$.

The domain of the function consists of all numbers. The independent variable is $t$, the dependent variable $N$.

It holds that $N(5)=2\cdot 5+3=13$.