SOLUTION: Explain how to write a function rule from the table below. Then write a function. X 2 4 6 ________ Y 1 0 -1

X|2  4  6
---------
Y|1  0 -1

We may notice that if we take half of the x's, we get
1,2,3, and subtract 2 from them you get -1,0,1, which are 
the y's with opposite signs.  So we can figure a rule 
like this

Take half of each x, 

x

subtract 2, 

x - 2

then multiply by -1

-1[x - 2]

x + 2

Then we would write

f(x) = x + 2 

But it takes a lot of thinking and intuition to come up with that
doing it that way.

-----------------------------------------------------

Here's a way that doesn't take so much intuition.

If we plot those three points (2,1), (4,0), (6,-1) on an
xy coordinate system, we see that we can draw a line through
them



so we take 2 of those points and find the equation of the line that passes
through them.  Say (2,1) and (4,0) 

Use the slope formula:

m = 
where (x1,y1) = (2,1)
and where (x2,y2) = (4,0)

m =  = 

Point-slope formula:

y - y1 = m(x - x1)

where (x1,y1) = (2,1)

y - (-1) = (x - 2)

y + 1 = x + 1

y = x + 2

f(x) = x + 2

Edwin