1. (a) Is the following association a function? Explain why or why not. Pick a 3

Question

1. (a) Is the following association a function? Explain why or why not. Pick a 3-digit positive integer with all three digits different. Reverse the digits to get another 3-digit number. Subtract the smaller number from the larger to get another positive number. If the difference is less than 100, insert leading zeros so you have three digits (e.g., 71 becomes 071). Reverse the digits of the difference and add it to the difference to get a final 3-digit number. 2. (a) Write an algebraic expression for the Magical Birthday Calculation Function defined by the following sequence of algebraic operations:

Explanation / Answer

To get the greatest difference, we want to subtract a small number from a large one, so we will need the digit 9 and the digit 1, in order to make a number in the 100’s and a number in the 900’s. The large number will look like 9N1 and the small number will look like 1N9, where N is a digit from 2 to 8. You will find that, no matter what you make N, the difference is 792. Hence domain = R range = 792 It is a function.

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