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2 function machines, arranged so that, the output from the top machine, with rule labeled, L, of x, becomes the input for the bottom machine, with rule labeled, r, of x.Lacey and Richens each have a personal function machine. Lacey’s machine, , squares the input and then subtracts . Richens’ function machine, , adds to the input and then multiplies the result by .

  1. Write equations that represent and .

  2. Lacey and Richens decide to connect their two machines so that Lacey’s output becomes Richens’ input. If is the initial input, what is the final output?

  3. What if the order of the machines is changed? Would it change the output? Justify your answer.

    Try computing the result for if the order is reversed.