Introduction to Functions: Practice Exercises

Here are various Exercises to accompany the section Introduction to Functions.  Some Exercises are designed to be done with a partner and to be graded by the partner.

  1. Consider the Ferris wheel example from the previous section.  Use an appropriate test from the text to explain why that relation is not a function, based on each of its following descriptions:
    1. As a graph:

    2. As a list of ordered pairs.
    3. As a formula: .
    4. As a table of values:
      x y
      0
      0
      45
      -45
      27
      27
      ·
      ·
      ·      		 103
      13
      58
      58
      94
      22
      ·
      ·
      ·
    5. As an arrow diagram.  Note: While you will not be able to given the entire diagram (since that would have an infinite number of entries), you should draw enough to support your explanation.

    Solution.

  2. Decide whether or not each of the following relations is a function, and explain your answer to your partner, using one of the tests from the text.
    1. The relation given by the table:
      x y
      -3
      -2
      -1
      0
      1
      2
      3      		 2
      0.5
      0
      0.5
      2
      4.5
      8
    2. The relation which is the reverse of that in part a).
    3. The relation given by the following arrow diagram:

    4. The relation given by ordered pairs (x, y) which satisfy the equation x + 2y = 21.
    5. The relation given by the following arrow diagram:

    Solution.

  3. Decide whether or not each of the relations that you constructed in the exercises for the previous section, and explain your answer to your partner, using one of the tests from the text.

    Solution.

Go to Functional Notation and Terminology .

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