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I don't know that you can do it just by looking at one. (At least, I'm not clever enough with arithmetic to do that.) But it's possible to do it using some simple aritmetic. Here's an input-output table.

5 38

6 45

7 52

8 59

The first thing I notice is that the numbers in the left-hand column are evenly spaced; the difference between any two of them is just one. The differences between all of the numbers in the right-hand column are also all the same, seven. So this input-output table represents a linear function.

In case you're working in a slightly more advanced situation here's another example:

3 11

7 23

9 29

13 41

In this case the left-hand column numbers are not evenly spaced and I can't just look at the differences between the numbers on the left. However, there's a slightly more advanced technique that I can apply.

( 23 - 11 ) / ( 7 - 3 ) = 12 / 4 = 3

( 29 - 23 ) / ( 9 - 7 ) = 6 / 2 = 3

( 41 - 29 ) / ( 13 - 9 ) = 12 / 4 = 3

The three slopes are the same. Therefore, the input-output table represents a linear function.

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โˆ™ 2013-11-19 17:16:35
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Q: How would you know if a function is linear or non-linear just by looking at a input-output table?
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