Functions, Domain and 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.

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