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**pellerinb****Member**- Registered: 2012-12-26
- Posts: 43

Hi all,

I have this function's shape in mind...

plot y = |(x-5)|^[1-|(x-5)|] from x=0 to 5

Anyone seen this kind of curve before in a similar (i.e. simpler) function? I really had to "mess around" to make it lol!

math is fun! :-D

Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.

In biology, we use math like we know what we are talking about. Sad isn't it.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,727

Hi;

This is what I got:

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**pellerinb****Member**- Registered: 2012-12-26
- Posts: 43

Yes... so... I'm just wondering if you have seen this shape elsewhere in a simpler function (I'm not considering the rest, just this part of the plot as you got).

Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.

In biology, we use math like we know what we are talking about. Sad isn't it.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,727

The general shape looks like a skewed Standard Normal Curve. Sort of like the ones that are produced for Chi Square.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**pellerinb****Member**- Registered: 2012-12-26
- Posts: 43

That's true... do you have an equation in mind?

Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.

In biology, we use math like we know what we are talking about. Sad isn't it.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,727

Hi;

I might be able to fit one of those forms to that curve but why would that equation be better than the one we used to generate the curve?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**pellerinb****Member**- Registered: 2012-12-26
- Posts: 43

Very true. I guess if I represent it as

y = |x|^[1-|x|] from x=-5 to 0

It looks more simple and orderly

In biology, we use math like we know what we are talking about. Sad isn't it.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,727

Hi;

You could simplify that a bit to

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**pellerinb****Member**- Registered: 2012-12-26
- Posts: 43

Whoa! That is good, bobbym. Thank you!

In biology, we use math like we know what we are talking about. Sad isn't it.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,727

I only tested it from -5 to 0, so use with caution.

Mathematica believes that is true for x≤0. I would try to prove that first.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**pellerinb****Member**- Registered: 2012-12-26
- Posts: 43

What type(s) of function(s) would it be? I assume it is a power function and an exponential function.

In biology, we use math like we know what we are talking about. Sad isn't it.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,727

Hi pellerinb;

I am not following you.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**pellerinb****Member**- Registered: 2012-12-26
- Posts: 43

Would it be a power function because it is y = | x ^...|

...likewise, would it be an exponential function because it has a variable in the exponent? Just curious.

In biology, we use math like we know what we are talking about. Sad isn't it.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,727

Hi;

You mean this expression?

You mean is it a function? Or would you like to approximate that with a something else?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,016

bobbym wrote:

Hi;

You could simplify that a bit to

That does not look correct.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,727

It is a simplification of his answer in post #7. They are algebraically the same but not numerically!

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,016

They are not algebraically the same either!

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,727

Have you plotted both?

Also

```
FullSimplify[Abs[x]^(1 - Abs[x]) == Abs[x^(1 + x)], {x <= 0}]
True
```

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**pellerinb****Member**- Registered: 2012-12-26
- Posts: 43

bobbym wrote:

Hi;

You mean this expression?

You mean is it a function? Or would you like to approximate that with a something else?

Yup, I mean, is it a function or what kind of function is it?

In biology, we use math like we know what we are talking about. Sad isn't it.

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,016

Yes, it is a function, but it does not have any particular name.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**pellerinb****Member**- Registered: 2012-12-26
- Posts: 43

Thanks!

In biology, we use math like we know what we are talking about. Sad isn't it.

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,016

You are welcome.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,727

It does now have a name.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**pellerinb****Member**- Registered: 2012-12-26
- Posts: 43

It appreciates being addressed by unsaid name.

In biology, we use math like we know what we are talking about. Sad isn't it.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,727

The unsaid function is what it shall be called henceforth.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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