- #26

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But if, as you are saying, they are both functions, how does one represent non-functional graphs? (is my wording right? I'm trying to pick stuff up here.)

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- Thread starter lLovePhysics
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- #26

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But if, as you are saying, they are both functions, how does one represent non-functional graphs? (is my wording right? I'm trying to pick stuff up here.)

- #27

Gib Z

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- #28

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But if, as you are saying, they are both functions, how does one represent non-functional graphs? (is my wording right? I'm trying to pick stuff up here.)

Okay, okay. I think people are getting confused here. Here's my take on it:

A

A

You can graph any equation, but that does not make it a function. You can graph a circle, and in order to do so you'd just draw a circle on the graph. A circle, though, is

- #29

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function:

[tex]y=\sqrt{x}[/tex]

Because it always gives the positive root,

not function:

[tex]y=\pm\sqrt{x}[/tex]

Because it gives two answers for each x.

Despite the curse of a useless GCSE curriculum, I think I've finally got it. Also, LaTeX is really freaking cool.

- #30

cristo

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Of course. In the above I may have mixed up talking about y=sqrtx and y=sqrtx-4. However, the important point still holds-- the graph of y=sqrtx-4 is not a "tipped over" parabola.

- #31

HallsofIvy

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Once again, no one said you can[t graph a relation that is not a function. A circle is the graph of a relation that is not a function. It fails the "vertical line test": any vertical line that passes through the graph does so only once.

The graph of (y+4)^{2}= x is a "parabola lying on its side" but y is NOT a function of x. If x= 4, then y can be either -2 or -6: the vertical line x= 4 passes through the graph at both (4,-2) and (4,-6).

However, the**function** [itex]y= \sqrt{x}[/itex] is defined as "the **positive** number whose square is x" and is a function. Then [itex]y= \sqrt{x}- 4[/itex] is the **part** of a parabola that starts at (0,-4) and rises upward and two the right. The functions domain is [itex][0,\infty)[/itex] and its range is [itex] [-4,\infty)[/itex].

The graph of (y+4)

However, the

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- #32

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- #34

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Remember, every real number has a positive and a negative square root. Don't feel too bad about that mistake, most graphing application programmers seem to forget as well.

So, basically, it should look a bit like y=x^2 tipped on its side.

What do you mean bit like y=x^2.

you mean half parabola in 4th quadrant.

- #35

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Think of it as the branch of y = x^2 that is in the 1st quadrant "flipped" over y = x.

- #36

HallsofIvy

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No, they haveWhat's so important about functions anyways? All they have are two y outputs for every x input right? Would it make a big difference (and get marked wrong) if I drew a horizontal parabola rather than just the top half??

There is nothing terribly important about "functions" (except that they are somewhat simpler than "relations") in mathematics but they tend to be very important in applications of mathematics to science because of the requirement of "repeatability": if you do an experiment twice, with everything set up exactly the same way, you should get exactly the same result- one input, one output. "This causes that" gives functions.

Think of it this way: If you were to go to a store and find different products that had the same price, you would not be surprised, right? The "product" is not a function of the price. On the other hand, if you found exactly the same product, same size, brand, and everything, in the same store for

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