## Functions, Domain & Codomain

A function is an operation that assigns to each number in a domain, a unique number in a codomain. The function is usually given in the form of an equation, for example, Each value of gives 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 to values 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 at so cannot be equal to -1) and codomain If the graph tends toward an or value without reaching it, then that value cannot be in the domain or codomain respectively.  