Functions and Transformations — Quiz

Question 1 • Precalculus

Which graph represents an odd function?

Answer

Image with description On a coordinate plane, a line curves down from quadrant 2 through (negative 2, 0) to (negative 1.5, negative 6). It then curves up through (negative 1, negative 5) through (0, 0) to (0.5, 0.4). It then curves down to (1, 0) and then curves up through (1.5, 2).

Image with description On a coordinate plane, a line curves up from quadrant 3 through (negative 2, 0) to (negative 1.6, 1.3). It then curves down through (0, 0) to (1.4, negative 1.3) and curves up through (2, 0).

Explanation

An odd function has rotational symmetry about the origin: whenever (x, y) is on its graph, (−x, −y) should also be on it. Graph B has this pattern, with its curve passing through the origin and the parts on opposite sides matching in opposite directions. Graph A does not: for example, it has points near (−1, −5) and (1, 0), which are not opposites.

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