Session 3, Part E:
Other Kinds of Functions (45 minutes)

In This Part: Functions and Non-Functions | More Functions | A Geometric Function

 So far you have been thinking about functions as algorithms or machines. They take an input -- in the cases you have seen, a number -- and give an output. Note 6 A function is really any relationship between an input variable and an output variable in which there is exactly one output for each input. Not all functions have to work on numbers, nor do functions need to follow a computational algorithm. Below are some examples of functions and non-functions. Read through them, then answer Problems E1-E4. Note 7 The following relationships are functions. Input: an integer Output: classification of the input as even or odd Input: a person's Social Security number Output: that person's birth date Input: the name of a state Output: that state's capital Input: the side length of a square Output: the area of that square Input: a word Output: the first letter of that word Problem E1 For each function described above, make a table of 5 or 6 input/output pairs. Explain why for every possible input there is only one possible output.

 Problem E2 In any of your tables, do you have repeated outputs? That is, do you have two different inputs that give the same output? The following relationships are not functions. Input: a number Output: some number less than the input Input: a whole number Output: a factor of the input Input: a person Output: the name of that person's grandparent Input: a city name Output: the state in which that city can be found Input: the side length of a rectangle Output: the area of that rectangle Input: a word Output: that word with the letters rearranged

 Problem E3 For each relationship described above, make a table of 5 or 6 input/output pairs. Explain why for some inputs there may be more than one possible output.

 Be sure to generate pairs of inputs and outputs that show that the relationship is not a function. What property would those pairs have?   Close Tip Be sure to generate pairs of inputs and outputs that show that the relationship is not a function. What property would those pairs have?

 Problem E4 Come up with three more examples of relationships that are functions, and three examples of relationships that are not functions. For each relationship, explain why it is or is not a function.

 Problems in Part E taken from IMPACT Mathematics Course 3, developed by Education Development Center, Inc. (New York: Glencoe/McGraw-Hill, 2000), p. 489. www.glencoe.com/sec/math
 Session 3: Index | Notes | Solutions | Video