Each person in a group picks a natural number and uses it as an input in the following f...

Each person in a group picks a natural number and uses it as an input in the following function machine:

a. Compare your answers. Based on the answers, make a conjecture about the range of the function.

b. Based on your answer in (a), graph the function.

c. Write the function in the simplest possible way using f(x) notation.

d. Justify your conjecture in (a).

e. Make up similar function machines and try different inputs in your group.

f. Devise a function machine in which the machine performs several operations but the output is always the same as the input. Exchange your answer with someone in the group and check that the other person's function machine performs as required.