Math Is Fun Forum

pellerinb

Member

Registered: 2012-12-26

Posts: 43

Anyone know of a function like this?

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

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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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Anyone know of a function like this?

Hi;

This is what I got:

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

pellerinb

Member

Registered: 2012-12-26

Posts: 43

Re: Anyone know of a function like this?

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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Anyone know of a function like this?

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.
Always satisfy the Prime Directive of getting the right answer above all else.

pellerinb

Member

Registered: 2012-12-26

Posts: 43

Re: Anyone know of a function like this?

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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Anyone know of a function like this?

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.
Always satisfy the Prime Directive of getting the right answer above all else.

pellerinb

Member

Registered: 2012-12-26

Posts: 43

Re: Anyone know of a function like this?

Very true. I guess if I represent it as

y = |x|^[1-|x|]  from x=-5 to 0

It looks more simple and orderly

---

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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Anyone know of a function like this?

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.
Always satisfy the Prime Directive of getting the right answer above all else.

pellerinb

Member

Registered: 2012-12-26

Posts: 43

Re: Anyone know of a function like this?

Whoa! That is good, bobbym. Thank you!

---

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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Anyone know of a function like this?

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.
Always satisfy the Prime Directive of getting the right answer above all else.

pellerinb

Member

Registered: 2012-12-26

Posts: 43

Re: Anyone know of a function like this?

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

---

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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Anyone know of a function like this?

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.
Always satisfy the Prime Directive of getting the right answer above all else.

pellerinb

Member

Registered: 2012-12-26

Posts: 43

Re: Anyone know of a function like this?

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.

---

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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Anyone know of a function like this?

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.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Anyone know of a function like this?

Hi;

You could simplify that a bit to

That does not look correct.

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“Here lies the reader who will never open this book. He is forever dead.
“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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Anyone know of a function like this?

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.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Anyone know of a function like this?

They are not algebraically the same either!

---

“Here lies the reader who will never open this book. He is forever dead.
“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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Anyone know of a function like this?

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.
Always satisfy the Prime Directive of getting the right answer above all else.

pellerinb

Member

Registered: 2012-12-26

Posts: 43

Re: Anyone know of a function like this?

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?

---

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.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Anyone know of a function like this?

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

---

“Here lies the reader who will never open this book. He is forever dead.
“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.

pellerinb

Member

Registered: 2012-12-26

Posts: 43

Re: Anyone know of a function like this?

Thanks!

---

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.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Anyone know of a function like this?

You are welcome.

---

“Here lies the reader who will never open this book. He is forever dead.
“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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Anyone know of a function like this?

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.
Always satisfy the Prime Directive of getting the right answer above all else.

pellerinb

Member

Registered: 2012-12-26

Posts: 43

Re: Anyone know of a function like this?

It appreciates being addressed by unsaid name.

---

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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Anyone know of a function like this?

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.
Always satisfy the Prime Directive of getting the right answer above all else.