Name DateWORKSHEET 8.1: DETERMINING IF A RELATION IS A FUNCTION
-------------------------------------------------------------------------------------Follow the steps below to determine if a relation is a function:- 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.’’
- If each value ofxis paired with exactly one value ofy, the relation is a function.
- 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, 3), (2, 4), (3, 5), (4, 6) 2. (1, 1), (1, 2), (1, 3), (1, 4)
- (1, 1), (2, 2), (3, 3), (4, 4) 4. (0, 0), (2, 4), (2,−4), (3,−9)
- (3, 2), (3,−2), (4, 15), (4,−15) 6. (−2,−8), (−1,−1), (1, 1), (2, 8)
- (2, 0), (2, 4), (2,−4), (4, 2) 8. (0, 0), (1, 1), (4, 2), (9, 3)
- (−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.275Copyright
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2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.