SOLUTION: Take a look at the table below and write out an equation for f(x). Show your work. x -3 -2 1 3 4 f(x) 0 3 12 18 21

Algebra ->  Functions -> SOLUTION: Take a look at the table below and write out an equation for f(x). Show your work. x -3 -2 1 3 4 f(x) 0 3 12 18 21       Log On


   

Question 342353: Take a look at the table below and write out an equation for f(x). Show your work.
x -3 -2 1 3 4
f(x) 0 3 12 18 21
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Take a look at the table below and write out an equation for f(x). Show your work.
x -3 -2 1 3 4
f(x) 0 3 12 18 21
----
f(x) = 3x+9 where Domain = {-3,-2,1,3,4}
==========================================
Cheers,
Stan H.

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

  x	-3	-2	1	3	4
f(x)	0	 3	12	18	21

One way is to plot the points and see what the graph looks like



Hmm!  Looks like a straight line could be drawn through all
5 of those points.  I'll get my ruler and green pen and see:



Sure looks like a straight line to me.  So I'll just find the equation
of the line that goes through, say, the first two points (any two
of the points would do).

(-3,0), (-2,3)

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29

m=%28%283%29-%280%29%29%2F%28%28-2%29-%28-3%29%29

m=3%2F%28-2%2B3%29

m=3%2F%28-1%29

m=3

Then I'll substitute that in the point-slope form:

y-y%5B1%5D=m%28x-x%5B1%5D%29

y-0=3%28x-%28-3%29%29

y=3%28x%2B3%29

y=3x%2B9

That's the answer.

Let's check to see if it works with all 5 points:

Substituting (-3,0)

y=3x%2B9
0=3%28-3%29%2B9
0=-9%2B9
0=0

Substituting (-2,3)

y=3x%2B9
3=3%28-2%29%2B9
3=-6%2B9
3=3

Substituting (1,12)

y=3x%2B9
12=3%281%29%2B9
12=3%2B9
12=12

Substituting (3,18)

y=3x%2B9
18=3%283%29%2B9
18=9%2B9
18=18

Substituting (4,21)

y=3x%2B9
21=3%284%29%2B9
21=12%2B9
21=21

Yeppers, it works for all 5 points,
so the equation is 

y = 3x + 9

Edwin