A function specifies a

More precisely:

A

The

It's helpful to think of a function as a

The most common method for visualising a function is its graph; which consists of all points $(x,y)$ in the coordinate plane such that $y=f(x)$ and $x$ is in the domain of $f$.

The graph of a function $f$ gives us a useful picture of the behavi…

**rule**by which an**input**is converted to a unique**output**.More precisely:

A

**function**$f$ is a rule that assigns to each element $x$ in a set $D$ exactly one element, called $f(x)$, in a set $E$.The

**domain**of a function is the set of all possible $x$ values that can be used as inputs, and the**range**is the set of all possible $f(x)$ values that arise as outputs.It's helpful to think of a function as a

**machine**(see Figure 1). If $x$ is in the domain of the function then when enters the machine, it is accepted as an input and the machine produces an output according to the rule of the function. Thus we can think of the domain as the set of all possible inputs $x$ and the range as the set of all possible outputs $f(x)$.The most common method for visualising a function is its graph; which consists of all points $(x,y)$ in the coordinate plane such that $y=f(x)$ and $x$ is in the domain of $f$.

The graph of a function $f$ gives us a useful picture of the behavi…