Question 622410
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The definition of a function demands that the function be able to map any given input value, *[tex \LARGE x], to one and only one output value, *[tex \LARGE y].


So, if you have a relationship between *[tex \LARGE x] and *[tex \LARGE y] such that for whatever value of *[tex \LARGE x] you are given, you can tell for certain what the value of *[tex \LARGE y] must be, then you have a function.  On the other hand, if you have a relation where there is a certain *[tex \LARGE x] value or set of *[tex \LARGE x] values where the value of the relation, *[tex \LARGE y], "could be this or it could be that", then you do NOT have a function.


Here is where the vertical line test comes in.  If you can find a vertical line anywhere that intersects the graph of your function in more than one place, you now have a "maybe this, maybe that" situation and you do NOT have a function.


Look at your graph.  The *[tex \LARGE y]-axis is certainly a vertical line, and your graph crosses the *[tex \LARGE y]-axis in two places, two being more than one.  So what is your conclusion?  Does the graph represent a function?


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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