SOLUTION: 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

Algebra ->  Functions -> SOLUTION: 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       Log On


   

Question 68854: 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
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

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:

 

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:

     y2 - y1
m = —————————
     x2 - x1

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

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

Now substitute in the point slope formula:

   y - y1 = m(x - x1)

   y - 1 = 3(x - 0)

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

 

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

    f(x) = 3x + 1

Edwin