Relationships Between Quantities — Test

Question 4 • Algebra II

Which graph represents an odd function?

Answer

Image with description On a coordinate plane, the x and y axes range from negative 6 to 6 in increments of 1. The graph has 11 points. The points are (negative 4 comma 3), (negative 4 comma 4), (negative 3 comma 5), (negative 2 comma 1) , (negative 1 comma negative 1), (0 comma negative 3), (1 comma negative 1), (2 comma 1), (3 comma 5), (4 comma 3), and (4 comma 4).

Image with description On a coordinate plane, the x and y axes range from negative 6 to 6 in increments of 1. The graph has 6 points. The points are (negative 5 comma 3), (negative 3 comma 1), (negative 1 comma 1), (1 comma 3), (3 comma negative 5), (5 comma negative 1).

Image with description On a coordinate plane, the x and y axes range from negative 6 to 6 in increments of 1. The graph has 8 points. The points are (negative 4 comma 0), (negative 3 comma 1), (negative 2 comma negative 3), (negative1 comma negative 2), (1 comma 2), (2 comma 3), (3 comma negative 1), and (4 comma 0).

Explanation

An odd function has rotational symmetry about the origin: whenever (x, y) is on its graph, (-x, -y) must also be on it. In choice C, the points (-4, 0) and (4, 0), (-3, 1) and (3, -1), (-2, -3) and (2, 3), and (-1, -2) and (1, 2) all match this rule. Therefore, choice C represents an odd function.

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