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
socannot be equal to -1) and codomain
If the graph tends toward an orvalue without reaching it, then that value cannot be in the domain or codomain respectively.
