Answer:
order: 2, 3, 1
Step-by-step explanation:
Reasonableness checks and your knowledge of integers and fractions will help you solve this. The offered questions are intended to help you think this through.
<h3>a.</h3>
For an output of -31, the machine (x -2)² cannot possibly be last. Its output can only be positive.
machine 2, (x-2)², cannot be last
Also, machine 3 cannot be last. For the output to be -31, the input to machine 3 must be -1/31. Neither of the other machines can produce a fraction with the inputs they might receive.
<h3>b.</h3>
For an input of x=0, the machine 1/x cannot possibly be first. 1/0 is undefined.
The other two machines will give the following outputs for an input of 0:
machine 1: 4(0) -32 = -32
machine 2: (0 -2)² = 4
It is unlikely that machine 1 will be first, because the other two machines cannot do anything useful with -32 as an input.
machine 3, 1/x, cannot be first
<h3>c.</h3>
The reasoning of part (a) tells you the last machine must be machine 1. The reasoning of part (b) tells you the first machine cannot be 3, so must be 2. The order of the machines must be ...
- machine 2: (0 -2)² = 4 . . . . . . . using an input of 0
- machine 3: 1/4 = 1/4
- machine 1: 4(1/4) -32 = -31 . . . . desired output
