Foundations of Euclidean Geometry — Test

Question 2 • Geometry

Which graph shows a set of ordered pairs that represent a function?

Answer

Image with description On a coordinate plane, solid circles appear at the following points: (negative 4, 2), (negative 2, 1), (negative 2, negative 1), (0, negative 2), (0, negative 4), (2, negative 5).

Image with description On a coordinate plane, solid circles appear at the following points: (negative 4, negative 4), (negative 2, 2), (1, 1), (2, negative 5), (4, negative 3), (4, 4).

Image with description On a coordinate plane, solid circles appear at the following points: (negative 2, 3), (negative 1, 2), (1, 1), (2, negative 1), (2, negative 3), (4, negative 5).

Image with description On a coordinate plane, solid circles appear at the following points: (negative 3, 2), (negative 2, 2), (0, 1), (1, 3), (2, negative 4), (4, negative 1).

Explanation

A set of ordered pairs represents a function when each x-value is paired with only one y-value. In choice D, the x-values −3, −2, 0, 1, 2, and 4 are all different, so every input has exactly one output. The other choices repeat an x-value with different y-values, so they are not functions.

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