Symmetry — Quiz

Question 10 • Algebra II

Which graph represents an even function?

Answer

Image with description On a coordinate plane, the x and y axes range from negative 5 to 5 in increments of 1. The graph has a parabola that opens down with a vertex at (0 comma 4). It goes through (negative 2 comma 0) and (2 comma 0).

Image with description On a coordinate plane, the x and y axes range from negative 5 to 5 in increments of 1. The graph has a straight line with a negative slope. It goes through (negative 2 comma 4), crosses the y axis at (0 comma 2), and crosses the x axis at (2 comma 0).

Image with description On a coordinate plane, the x and y axes range from negative 5 to 5 in increments of 1. The graph has 2 curves, one in quadrant 1 and the other in quadrant 3. The curve in quadrant 1 goes through points (1 comma 5) and (5 comma 1). The curve in quadrant 3 goes through points (negative 5 comma negative 1) and (negative 1 comma negative 5).

Image with description On a coordinate plane, the x and y axes range from negative 5 to 5 in increments of 1. The graph has a curve in the shape of W. It has four x intercepts at (negative 2 comma 0), (negative 1 comma 0), (2 comma 0), (3 comma 0), and a y intercept at (0 comma 2 point 5). The curve has asymptotes at x equals negative 3 and x equals 4. The curve is labeled as g of x.

Explanation

An even function has symmetry across the y-axis: whenever (x, y) is on its graph, (−x, y) is also on it. Choice A is a downward-opening parabola with its vertex at (0, 4), and it passes through both (−2, 0) and (2, 0), showing that symmetry. The other graphs do not have y-axis symmetry.

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