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## #1 2006-09-27 07:34:55

espeon
Real Member
Registered: 2006-02-05
Posts: 2,586

### function machine

function game!

just answer the questions and the first person to answer it right has to make a new question! (there has to be at least 4 examples and only do 1 question at a time)

1.

a                                                 b

9      ~~~~~~~~~~~~~~~~~    27
19    ~~~~~~~~~~~~~~~~~ 120.3
21    ~~~~~~~~~~~~~~~~~ 147
3     ~~~~~~~~~~~~~~~~~  3

now lets all make bets! who will do it first!

devante
mathsisfun
ganesh
patrick
zach
mathsyperson
insomnia
ricky
justlooking
or someone else i forgot!(note:this is due to my bad memory)

Last edited by espeon (2006-09-28 07:12:31)

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## #2 2006-09-27 08:09:02

Devantè
Real Member
Registered: 2006-07-14
Posts: 6,400

### Re: function machine

9      ~~~~~~~~(+18)~~~~~~~~~    27
19    ~~~~~~~~(+101.3)~~~~~~~~~ 120.3
21    ~~~~~~~~(+126)~~~~~~~~~ 147
3     ~~~~~~~~~(+0, or -0, or ÷1, or x1, or lots of other things)~~~~~~~~  3

I bet: me.

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## #3 2006-09-27 09:44:29

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,657

### Re: function machine

There is a square, and a division.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #4 2006-09-27 13:04:00

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: function machine

I like Devante's function better.  Less to think about

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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## #5 2006-09-27 20:45:03

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: function machine

MathsIsFun wrote:

There is a square, and a division.

Using your function would mean that one of your results is 1/30 away from Espeon's.

Why did the vector cross the road?
It wanted to be normal.

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## #6 2006-09-28 03:05:53

espeon
Real Member
Registered: 2006-02-05
Posts: 2,586

### Re: function machine

um i mean thats the same function on all of them to make it easier for you. im doing it in 4's. and mathsisfun is right

Presenting the Prinny dance.
Take this dood! Huh doood!!! HUH DOOOOD!?!? DOOD HUH!!!!!! DOOOOOOOOOOOOOOOOOOOOOOOOOD!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

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## #7 2006-09-28 03:31:22

Patrick
Real Member
Registered: 2006-02-24
Posts: 1,005

### Re: function machine

I'm obviously not the first to figure these out, but I just logged on, and no one has written them

Last edited by Patrick (2006-09-28 03:32:04)

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## #8 2006-09-28 03:35:18

Devantè
Real Member
Registered: 2006-07-14
Posts: 6,400

### Re: function machine

MathsIsFun wrote:

There is a square, and a division.

I think that was it.

That is the same as yours = b = a^2(/3)

First time in a long time I have seen LaTeX in hidden tags.

Last edited by Devanté (2006-09-28 03:36:47)

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## #9 2006-09-28 03:42:56

espeon
Real Member
Registered: 2006-02-05
Posts: 2,586

### Re: function machine

a is meant to be the start number and b is the second. and i dont understand that fraction thingy. mine isnt really that complicated...

Presenting the Prinny dance.
Take this dood! Huh doood!!! HUH DOOOOD!?!? DOOD HUH!!!!!! DOOOOOOOOOOOOOOOOOOOOOOOOOD!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

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## #10 2006-09-28 03:48:02

Devantè
Real Member
Registered: 2006-07-14
Posts: 6,400

### Re: function machine

b = a^2(/3).
a^2(/3) = b

It's the same thing.

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## #11 2006-09-28 04:06:55

espeon
Real Member
Registered: 2006-02-05
Posts: 2,586

### Re: function machine

ooooo i get it the fraction thing is supposed to be a division part thingy! Yep patrick won

Presenting the Prinny dance.
Take this dood! Huh doood!!! HUH DOOOOD!?!? DOOD HUH!!!!!! DOOOOOOOOOOOOOOOOOOOOOOOOOD!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

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## #12 2006-09-28 04:10:37

Devantè
Real Member
Registered: 2006-07-14
Posts: 6,400

### Re: function machine

Yep. a² ÷ 3 = b.

Last edited by Devanté (2006-09-28 04:11:01)

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## #13 2006-09-28 04:51:49

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: function machine

Does that mean that it's Patrick's turn to make a function now?

Why did the vector cross the road?
It wanted to be normal.

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## #14 2006-09-28 04:58:07

Patrick
Real Member
Registered: 2006-02-24
Posts: 1,005

### Re: function machine

I guess we could make it a game I'm kinda busy with school atm though, so if anyone else wants to make the next 'function-puzzle' they're welcome

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## #15 2006-09-28 07:08:27

espeon
Real Member
Registered: 2006-02-05
Posts: 2,586

### Re: function machine

ok then we can make it a game! ill edit the title. its patricks turn!

Presenting the Prinny dance.
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## #16 2006-09-28 07:13:17

espeon
Real Member
Registered: 2006-02-05
Posts: 2,586

### Re: function machine

nope i cant edit the title but i edited thefirst post lol

Presenting the Prinny dance.
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## #17 2006-09-28 07:56:15

Patrick
Real Member
Registered: 2006-02-24
Posts: 1,005

### Re: function machine

Here we go.. As before, b is a function of a
a - b
2 - -1
4 - 2
5 - 5
10 - 35

Last edited by Patrick (2006-09-28 07:56:44)

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## #18 2006-09-28 07:58:18

Patrick
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Registered: 2006-02-24
Posts: 1,005

### Re: function machine

ah, sorry ricky.. Guess you'll just have to answer my question fast then I'm pretty sure you know the function already.. hehe

edit: he deleted his post, that's why this might seem a bit weird

Last edited by Patrick (2006-09-28 07:58:57)

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## #19 2006-09-28 08:03:12

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: function machine

Yea patrick, you beat me in under a minute, little twerp

(a^2)/2 - 3/2 * a

Mine:

a    ->      b

1     ->     1
2     ->     4
3     ->     9
4     ->     73
5     ->     25
6     ->     36
.              .
.              .
.              .

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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## #20 2006-09-28 08:10:02

Patrick
Real Member
Registered: 2006-02-24
Posts: 1,005

### Re: function machine

that's correct, and simplified:

and you'll probably recognize it as the formula for finding the number of diagonals in a polygon with a sides.

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## #21 2006-09-28 09:38:56

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: function machine

Are we allowed any function we like, or does it have to be a nice one? Because technically, if you give any function with n examples of how it works, then there's always a polynomial of order (n-1) that will fit it.

In this case, that's 4.75n^5 - 80.75x^4 + 508.25x^3 - 1457.2x^2 + 1881x - 855.

I'm assuming Ricky thought of a nice one. He might have decided to be mean and done one of those multi-things.

{  73            If x=4
f(x) =  {
{   x²     Otherwise

Or it could also be some kind of sine wave, or addition of waves.

Why did the vector cross the road?
It wanted to be normal.

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## #22 2006-09-28 13:42:37

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: function machine

You're right mathsyperson.  The point being to show that not all functions have to be defined by a single formula.  But remember, when you see "..." it means that there is some pattern to follow.

It's your turn, mathsyperson.  I'll start preparing some more interesting ones.

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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## #23 2006-09-29 01:07:57

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: function machine

I'll have a go at making one then.

a  -->  b
1         3
2        -4
3        -11
4        -4
5         3

Why did the vector cross the road?
It wanted to be normal.

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## #24 2006-09-29 03:16:38

espeon
Real Member
Registered: 2006-02-05
Posts: 2,586

### Re: function machine

thats interesting.... i have absolutely no idea how to solver that. 2 and 4 come up with the same answer 1 and 5 come up with the same answer yet again and 3 is just singly. its like a pattern but still dont know how to solve it lol

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## #25 2006-09-29 03:22:31

Patrick
Real Member
Registered: 2006-02-24
Posts: 1,005

### Re: function machine

If you plot this, it might help you realise what kind of function this might be..

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