The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

(Marvins-Underground-K-12) #1
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WORKSHEET 8.1: DETERMINING IF A RELATION IS A FUNCTION
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Follow the steps below to determine if a relation is a function:


  1. Find thex-values andy-values of the ordered pairs.

    • Thex-values are the first numbers in ordered pairs. They are called the ‘‘domain.’’

    • They-values are the second numbers in ordered pairs. They are called the ‘‘range.’’



  2. If each value ofxis paired with exactly one value ofy, the relation is a function.

  3. If one value ofxis paired with two or more different values ofy, the relation is not a
    function.


EXAMPLES
(1, 2), (2, 4), (3, 6), (4, 8) is a function. Each value ofxis paired with exactly one value ofy.
(0, 0), (1, 1), (1,−1), (2, 2), (2,−2) is not a function. 1 is paired with 1 and−1 and 2 is paired
with 2 and−2.
(1, 1), (−1, 1), (2, 4), (−2, 4) is a function. Every value ofxis paired with one and only one value
ofy.
DIRECTIONS: State whether or not each relation is a function. If the relation is not a
function, tell why.


  1. (1, 3), (2, 4), (3, 5), (4, 6) 2. (1, 1), (1, 2), (1, 3), (1, 4)

  2. (1, 1), (2, 2), (3, 3), (4, 4) 4. (0, 0), (2, 4), (2,−4), (3,−9)

  3. (3, 2), (3,−2), (4, 15), (4,−15) 6. (−2,−8), (−1,−1), (1, 1), (2, 8)

  4. (2, 0), (2, 4), (2,−4), (4, 2) 8. (0, 0), (1, 1), (4, 2), (9, 3)

  5. (−4, 2), (0, 3), (−4, 4), (0, 5)


CHALLENGE:(−2, 5), (−1, 0), (0, 1), and (2, 5) is a function. If thex-values and
y-values of this function are switched, the relation that results is (5,−2), (0,
−1), (1, 0), and (5, 2). This is not a function. Provide an example of a function
that will still be a function if thex-values andy-values are switched.

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2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.

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