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When you see the actual function (e.g. f(x) = ...) you can know what each input corresponds to, and can construct any table. If you are given just the table, you cannot always predict the function correctly, since the function the table seems to represent does not necessarily have to be that function. For example, it might seem that

x : f(x)

-2 -4

-1 -2

0 0

1 2

2 4

would correspond to f(x) = 2x, but this is not necessarily the case. There could be some arbitrary function that just happens to contain those five points.

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Q: What is some advantages when you see a rule function rather than listing function values on a table?
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What are the advantages in using a rule for a function rather than listing function values in a table?

If the domain is infinite, it is not possible to list the function.


What is a table that is used to describe a function by listing all outputs?

It is generally referred to as "a table of values"


What advantages can you see of having a function rule instead of a table of values?

A table of values is no use if the domain is infinite.


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The domain of a function is the set of values for which the function is defined.The range is the set of possible results which you can get for the function.


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If your table has two columns--the left one listing various values for x, the "input," and the right one listing corresponding f(x) "output" values, let's say--make sure that there is only one output for every input: meaning there is only one number in each row of the right column.


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What Excel function sums values and then divides by the number of values?

The AVERAGE function.


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I'm afraid there is not.


The set of all values that a function will return as outputs is called the of the function?

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