Question 68854
<pre><font size = 5><b>
3.  Take a look at the table below and 
write out an equation for f(x).
x    -2  -1  0  1  2
f(x) -5  -2  1  4  7

Plot them:

 {{{ graph( 150, 300, -4, 4, -7, 9, -5+sqrt(.1-(x+2)^2),-2+sqrt(.1-(x+1)^2),1+sqrt(.1-(x-0)^2),4+sqrt(.1-(x-1)^2),7+sqrt(.1-(x-2)^2) ) }}}

They look like they all fall on a straight 
line, so pick any two of them and find the 
slope:

Say we pick the points (0,1) and (1,4)

Use the slope formula:

     y<sub>2</sub> - y<sub>1</sub>
m = —————————
     x<sub>2</sub> - x<sub>1</sub>

where (x<sub>1</sub>, y<sub>1</sub>) = (0, 1) and (x<sub>2</sub>, y<sub>2</sub>) = (1, 4)

     (4) - (1)     3     
m = ——————————— = ——— = 3
     (1) - (0)     1      

Now substitute in the point slope formula:

   y - y<sub>1</sub> = m(x - x<sub>1</sub>)

   y - 1 = 3(x - 0)

   y - 1 = 3x
       
       y = 3x + 1 

 {{{ graph( 150, 300, -4, 4, -7, 9, 3x+1,-5+sqrt(.1-(x+2)^2),-2+sqrt(.1-(x+1)^2),1+sqrt(.1-(x-0)^2),4+sqrt(.1-(x-1)^2),7+sqrt(.1-(x-2)^2) ) }}}

Now replace " y " with the functional notation " f(x) "

    f(x) = 3x + 1

Edwin</pre>