The next function we will explore is called the "Prime?" function. Most of you will remember that a prime number is a whole number that has only itself and one as factors. A few examples of prime numbers are 7, 13, and 29. Can you come up with some other examples?
Note 8
The number 6 is not a prime number, because it has 2 and 3 as factors. The number 11 is prime, because its only factors are 1 and itself. A prime number must have exactly two factors -- no more, no less. Close Tip
The "Prime?" function takes positive whole numbers as inputs and produces the outputs yes and no -- yes if the input is a prime, and no if the input is not a prime. Use what you know about functions and prime numbers to answer Problems E5-E11.
Problem E5
a.
If the input is 3, what is the output?
b.
If the input is 2, what is the output?
c.
If the input is 100, what is the output?
d.
If the input is 1, what is the output?
Remember, the output is either yes or no. Close Tip
Problem E6
If the output of the "Prime?" function is yes, what could the input have been?
If possible, describe a function that would undo the "Prime?" function. That is, if you put an input into the "Prime?" function and then put the output into your new function, you get back your original input.
Note 9
Note the relationship between Problems E6 and E8. Close Tip
Problem E9
The "3" function takes real numbers as inputs and always outputs the number 3.
a.
If the input is 17, what is the output?
b.
If the input is -2, what is the output?
c.
If the input is 1.5, what is the output?
The answers to all the parts of Problem E9 are all the same number. Close Tip
Problem E10
If the output is 3, what could the input have been?
Problem E11
Explain why "3" is a function.
Problem E12
If possible, describe a function that would undo the "3" function. That is, if you put an input into the "3" function and then put the output into your new function, you get back your original input.
Note the relationship between Problems E10 and E12. Close Tip
Problems in Part E taken from IMPACT Mathematics Course 3, developed by Education Development Center, Inc. (New York: Glencoe/McGraw-Hill, 2000).
