x,y

1, -2

2,-1

3,0

4,1

5,2

rule: y=x-3

x,y

-2,8

-1,5

0,4

1,5

2,8

rule: _____

x,y

-3,-13

-2,-9

-1,-5

0,-1

1,3

rule: _____

Help? Thanks!

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- Feb 7th 2008, 06:05 PMnathan02079Determine a rule for each table of values.
x,y

1, -2

2,-1

3,0

4,1

5,2

rule: y=x-3

x,y

-2,8

-1,5

0,4

1,5

2,8

rule: _____

x,y

-3,-13

-2,-9

-1,-5

0,-1

1,3

rule: _____

Help? Thanks! - Feb 7th 2008, 06:12 PMJhevon
- Feb 7th 2008, 06:15 PMnathan02079
"i can tell you what i thought about, but it was not really a mathematically rigorous process"

please tell me =) - Feb 7th 2008, 06:25 PMJhevon
as i said, this is not sure to get you the answer with things like this, i just lucked out. it is better to think of things this way before i went into the real mathematical process, which can get complicated computation-wise.

i looked at the 0's first. in the first problem, 0 --> 4. so i assume y = (some manipulation of x) + 4.

so then i subtracted 4 from all the other y-values, and tried to figure out what i would do to x to get them. i thought about multiplying by a negative number to make it positive, since all the negative numbers went to positive, but it did not work for all. so then i thought of squaring. and it worked!

same for the second. i saw 0 --> -1, so i thought y = f(x) - 1. after playing around a bit, 4x was the obvious choice

sorry i can't explain more, but i'm in a rush... - Feb 7th 2008, 06:28 PMnathan02079
- Feb 7th 2008, 06:53 PMSoroban
Hello, nathan02079!

I'll do the easier one first . . .

Quote:

The*first*differences are constant.

. . Hence, the function is of the*first*degree (linear).

The general linear function is: .

Use any two values from the table to set up a system of equations.

. .

Hence: .

Therefore: .

Quote:

. .

The*second*differences are constant.

. . Hence, the function is of the*second*degree (quadratic).

The general quadratic function is: .

Use any three values from the table to set up a system of equations.

. .

Then [1] and [3] become: .

Add [4] and [5]: .

Therefore: .