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Question 765563: f(1)=8,f(2)=-5,f(3)=1
I need to write the function as a ordered pair, giving the domain and range of f.
I am not understanding the whole concept of functions.
Found 2 solutions by jim_thompson5910, josgarithmetic:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! f(1)=8 ---> (1,8)
f(2)=-5 ---> (2,-5)
f(3)=1 ---> (3,1)
Function is
{(1,8), (2,-5), (3,1)}
Domain: {1, 2, 3}
Note: the domain is the set of possible x values
Range: {8, -5, 1}
Note: Range is the set of possible y values
Answer by josgarithmetic(39613) (Show Source):
You can put this solution on YOUR website! What kind of function? Three points tells very little. Line will not work because slopes are different between each consecutive pair of points. Do you want a parabola? Maybe possible because you have three points.
You need to know the equation of a suitable parabola for those three points before you can tell the function's domain and range.
You can try finding a parabola fit using general form of a parabola, y=ax^2+bx+c and treat the coefficients as the unknown variables.
Turn the members to alternate sides, and use as ax^2+bx+c=y.
a*1^2+b*1+c=8
a*2^2+b*2+c=-5
a*3^2+b*3+c=1
Solve this system for a, b, and c. Any method you want. substitution, elimination, matrices operations, whatever you want.
Not showing that portion of work here, the results are this:
(If not showing that work here is getting in the way, then that itself is a much separate problem).
Your parabola fit equation in general form is then 
WHAT TO DO NEXT:
Domain will be all real numbers.
Range is best found through completing the square to put the function into standard form and you should find that the range will be GREATER than some particular value, based on the vertex point, which can be read directly from the standard form equation.
(Knowing how to complete the square is also a very separate problem by itself).
Abbreviating much of the rest of that,
The square term to use for "completing the square" is (83/(2*19))^2. Adding and subtracting this to the general polynomial member and simplifying will give you  , the equation in standard form. The vertex is a minimum at
( 83/38, -809/152 );
The RANGE will be  .
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