## Functions, Domain & Codomain

A function is an operation that assigns to each numberin a domain, a unique numberin a codomain. The function is usually given in the form of an equation, for example,Each value ofgives a unique value of- if this were not so, we would not have a function. To sketch a function we need to find a set of points. This is most easily done by drawing up a table.

-3 | -2 | -1 | 0 | 1 | 2 | 3 | |

9 | 4 | 1 | 0 | 1 | 4 | 9 | |

+1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

10 | 5 | 2 | 1 | 2 | 5 | 10 |

If we have a graph of a function and we want to know the domain and codomain, then we can find them by looking at the axes. To find the domain, we look at the x-axis. To find the range or codomain we look at the- axis. For the function above, the function is restricted tovalues in the rang [-3,3] so the domain is the interval, [-3,3] and the codomain or range is the interval [1,10].

The graph below,has domain(notice the vertical dotted line, indicating that atsocannot be equal to -1) and codomainIf the graph tends toward an orvalue without reaching it, then that value cannot be in the domain or codomain respectively.