For a good explanation of what makes a function see

http://www.mathsisfun.com/sets/function.html

The early stuff on that page you will find trivial, so skip down to about half way.

The problem with using a graph plotter is caused by the way they work.

The domain for x is set and the lowest value calculated using the formula, and a point plotted.

Then x is given a small increment, a new point calculated, and a line is drawn from the first point.

This carries on for a sequence of points throughout the domain.

This is OK for many functions where the curve is continuous throughtout the domain.

If there is an asymptote the process can lead to incorrect plots.

For example, many plotters doing y = tanx try to connect a point at x just less than pi/2 to a point just over pi/2 and end up with a nearly vertical line at the discontinuity.

There are fixes that improve the plotting to avoid this.

http://www.mathsisfun.com/data/function-grapher.php

shows y = tanx correctly.

As your equation is not a function (more than one y for each x) you cannot use that plotter .

But MIF has also made a plotter that will handle it at

http://www.mathsisfun.com/data/grapher-equation.html

This shows no gap, even when you zoom in at (e,e).

(e,e) certainly is a valid point for the equation. (Any point on y=x is valid)

But it does show y = 0 as part of the curve and I'm not sure that is OK.

For me W/A looks ok and doesn't have y = 0.

Moral of this: Beware when you let a computer do your maths. Not all results are correct.

Bob

]]>Oh I see, so the distinction is that it can be many to one, but not one to many.

Yes. Another thing that must be satisfied by a function is that it must have a value at every element of its domain.

]]>Well, you would consider it as a function. For example:

y2 = 2x to y2 = 4ax form, y2 = 4 (2/4) x

I know that y^2 = 4ax is the general form of a parabola, I was just asking why it was not a function...

So, what is an example of a function that is not one-to-one?

]]>y2 = 2x to y2 = 4ax form, y2 = 4 (2/4) x]]>

I will try plotting it like that.

]]>No, it is a function.

Why?

Plot it with W|A, but tell it to show the graph in the range x = 2 to x = 3, or x = 2.5 to x = 3.

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