Which statement describes an even function?

Which statement describes an even function?

• A. Symmetric with respect to the origin
• B. Symmetric with respect to the x-axis
• C. It has a horizontal tangent at zero
• D. Symmetric with respect to the y-axis

Answer: (D)

Even functions have symmetry about the y-axis, meaning the graph looks the same when x is replaced by -x. This is captured by the condition f(-x) = f(x) for all x in the domain. The statement describing symmetry with respect to the y-axis matches this idea, so it is the correct description of an even function. For contrast, symmetry about the origin describes odd functions (f(-x) = -f(x)), symmetry about the x-axis would force the graph to reflect across the x-axis, which isn’t a general property of most functions, and a horizontal tangent at zero relates to the slope at x = 0, not the overall symmetry.

Even functions have symmetry about the y-axis, meaning the graph looks the same when x is replaced by -x. This is captured by the condition f(-x) = f(x) for all x in the domain. The statement describing symmetry with respect to the y-axis matches this idea, so it is the correct description of an even function.

For contrast, symmetry about the origin describes odd functions (f(-x) = -f(x)), symmetry about the x-axis would force the graph to reflect across the x-axis, which isn’t a general property of most functions, and a horizontal tangent at zero relates to the slope at x = 0, not the overall symmetry.