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Learning Math Home
Patterns, Functions, and Algebra
Session 3 Part A Part B Part C Part D Part E Homework
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Session 3 Materials:

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.

Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
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


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

Next > Part E (Continued): More Functions

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