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Question 18 • Test

Which graph represents an odd function?

Answer
A
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).
B
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).
C
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).
D
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 2), (negative 3 comma negative 1), (negative 1 comma negative 3), (0 comma 1), (1 comma 0), (2 comma negative 4), (4 comma 5), and (5 comma 4).

Explanation

An odd function satisfies f(-x) = -f(x), so its points come in pairs reflected through the origin. In choice B, for example, (-3, 1) pairs with (3, -1), and (-2, -3) pairs with (2, 3); the points at x = -4 and x = 4 both have y = 0. Thus choice B represents an odd function.

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