Consider the function machine that accepts inputs as ordered pairs. Suppose the components of the ordered pairs are natural numbers and the first component is the length of the rectangle and the second is its width. The following machine computes the area of the rectangle. Thus for a rectangle whose length L, is 3 and whose width, W, is 2, the input is (3,2) and the output is 3 x 2 or 6. Answer each of the following questions:
a. For each of the following inputs, find the corresponding outputs: 1) (3,4) 2) (4,3) 3) (6,2) 4) (1,12)
b. Find the set of all inputs for which the output is 20.

Question

Consider the function machine that accepts inputs as ordered pairs. Suppose the components of the ordered pairs are natural numbers and the first component is the length of the rectangle and the second is its width. The following machine computes the area of the rectangle. Thus for a rectangle whose length L, is 3 and whose width, W, is 2, the input is (3,2) and the output is 3 x 2 or 6. Answer each of the following questions: 
a. For each of the following inputs, find the corresponding outputs: 1) (3,4) 2) (4,3) 3) (6,2) 4) (1,12) 
b. Find the set of all inputs for which the output is 20.

anonymous · Answer

oops and forgot c.  what are the domain and range of the function?

directrix · Answer

Do you have your answers for part a handy?

anonymous · Answer

if I did that part correctly the answer for all of a. is 12

directrix · Answer

That's what I got.

directrix · Answer

On b) you need the factors of 20, that is, pairs of whole numbers that multiply to 20.

anonymous · Answer

I find 6 pairs that equal 20 for part b.

directrix · Answer

Yes, and you see that  (1,20) and (20,1) count as two separate inputs.

anonymous · Answer

yes, (20,1), (1,20), (4,5), (5,4), (2,10), and (10,2), but it is c. that is throwing me.  I'm not sure if I am just over thinking it

directrix · Answer

The function is the area function for a rectangle: y = L*W.

directrix · Answer

Domain is the set of acceptable values of a relation. (the relation in this case is a function)

Range is the set of possible values of a relation.

directrix · Answer

My best take on the domain is the set of natural numbers. The range would be the same.

anonymous · Answer

ok, thanks.  This is one that keeps me guessing.  I could get through the first two parts, but felt really lost for portion c.

directrix · Answer

I'm rethinking part c in terms of the "input machine." Loosely said, the domain of a function could be thought of as what can go in and the range as what can come out after the machine "processes" what went in.

Consider the function machine that accepts inputs as ordered pairs.

I will rephrase the domain.

D = the set of all ordered pairs (L,W) where L and W are natural numbers.

R = the set of natural numbers.

anonymous · Answer

thank you for clarifying even more, much appreciated!