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I guess the reason we use function notation f(x) because it gives us more information about the function. For example, if you have a function : y = 5x + 10, and you have find y values with a long list of x, it's hard to keep track which x you are calculating. In that case, function notation help you a lot. If you have x = 1, you simply write f(1) = 5 x 1 + 10, or x = 10, it will be f(10) = 5 x 10 + 10; so when you look back at the calculation, you will find it easier see all the values.

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Q: Why do we use function notation?
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Function notation means the function whose input is x. The mathematical way to write a function notation is f(x).


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