in-out table

[stance]

I have a problem with in-out table:

   in | out
  ----|-----
    1 |  2
    2 |  5

I am feeling lost and would appreciate some help. Thank you.

 

[stapel]

So... what is the problem you're having? Are you supposed to be doing something with the table...?

Eliz.

 

[stance]

in out

find as many rules as yhou can that fit both rows of thes table
write a rule for each table that tellswhat to do with the in to get the out
exopress each rule as a compete sentence such as the out is one more than four times the in

 

[Denis]

1 : 2 The out is twice the in.
2 : 5 The out is 1 + twice the in

Were you unable to "see" that?

 

[soroban]

Hello, stance!

   in | out
  ----|-----
    1 |  2
    2 |  5

Here's one approach . . .

When the \(\displaystyle x\) (In) "goes up by 1", the \(\displaystyle y\) (Out) "goes up by 3".

The rule could be: \(\displaystyle \,y\:=\:3x\)

But it doesn't quite fit:
. . \(\displaystyle 3\,\times\,1\:=\:3\) . . . and we want \(\displaystyle 2.\)
. . \(\displaystyle 3\,\times\,2\:=\:6\) . . . and we want \(\displaystyle 5.\)

Our formula gives answers which are too big by 1.

Very well, we modify our rule: \(\displaystyle \,y\:=\:3x\,- \,1\)
. . (Multiply the In by 3, and subtract 1.)

And there is one possible rule.


Here's another: \(\displaystyle \,y\:=\:x^2\,+\,1\)
. . (Square the In, and add 1.)