Which set of ordered pairs in the form of (x, y) does not represent a function of x?

a. {(1, 1.5), (2, 1.5), (3, 1.5), (4, 1.5)}

b. {(0, 1.5), (3, 2.5), (1, 3.3), (1, 4.5)}

c. {(1, 1.5), (–1, 1.5), (2, 2.5), (–2, 2.5)}

d. {(1, 1.5), (–1, –1.5), (2, 2.5), (–2, 2.5)}

The correct answer is B. This set of points is not a function.

By definition, a function represents the relationship between two different variables: x and y. It associates each element/value of the set X (the domain of the function), with a unique value of the set Y.

The coordinates listed in the question represent points in each of the functions A-D. In each pair, the first value listed represents an X-value and the second is referred to an Y-value.

Each value of the domain X, cannot correspond to more than one Y value, and this is exactly happening in B.  For the value x=1, two different y-values are listed: y1=3.3 and y=4.5. Therefore, this sucession of coordinates does not match the definition of function, and cannot be a function.

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