Explain what a function is and how to determine whether tables, graphs, equations, and ordered pairs are a function.

In order to define a function, you need two sets, say and . will be the domain, i.e. the "starting" set. will be the range (or co-domain), and you can think of this as the "landing" set.

A function is a rule that maps, following the same logic, every element of into one and only one elment of .

Most of the time, you'll deal with numeric function, i.e. functions that take a number as input and give another number as output. For example, writing

means that your function takes a certain number as input, and return twice that number, , as output.

Finally, a function can also be described by explicit pair of inputs and outputs. For example, defining a function with the table

means that maps 1 onto 2, 4 onto 6 and 7 onto 89. Such a collection of pairs is actually a function if:

(1) for example, if your domain is , and the range is , the table

does not represent a function from to , because 4 is in the domain, but it is not mapped into anything. Similarly, the table

is not a valid function, because 4 is mapped onto 89, which is not in the range.

(2) for example, using the same sets as above, the table

does not represent a function from to , because 1 is mapped into both 13 and 14, but a value in the domain can be mapped into only one value in the range.

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step-by-step explanation:

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