Practice Test

Question 1 • Algebra II

Which graph represents an even 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 7 points. The points are (negative 4 comma negative 3), (negative 3 comma negative 5), (negative 2 comma 1), (0 comma 0), (2 comma 1), (3 comma negative 5), and (4 comma negative 3).

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).

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 7 points. The points are (negative 3 comma negative 6), (negative 2 comma negative 4), (negative 1 comma negative 2), (0 comma 0), (1 comma 2), (2 comma 4), and (3 comma 6).

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 7 points. The points are (negative 5 comma 2), (negative 4 comma 1), (negative 3 comma 3), (negative 2 comma 5), (2 comma negative 2), (3 comma negative 5), (4 comma negative 6).

Explanation

An even function satisfies f(−x) = f(x), so its graph is symmetric about the y-axis. In choice A, the points at x-values −4 and 4 both have y = −3, the points at −3 and 3 both have y = −5, and the points at −2 and 2 both have y = 1; the point at x = 0 lies on the y-axis. Thus A represents an even function.

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