An even function satisfies f(-x) = f(x). Provide an example.

An even function satisfies f(-x) = f(x). Provide an example.

• A. f(x) = x
• B. f(x) = x^2
• C. f(x) = sin x
• D. f(x) = e^x

Answer: (B)

Even functions mirror across the y-axis, meaning f(-x) = f(x) for every x. A good example is f(x) = x^2. If you replace x with -x, you get (-x)^2 = x^2, which exactly matches f(x). For instance, f(3) = 9 and f(-3) = 9, so the values are the same on both sides of the axis. The other expressions don’t share this symmetry. For f(x) = x, f(-x) = -x, which isn’t the same as x except at x = 0. For f(x) = sin x, f(-x) = -sin x, again not equal to sin x except at x = 0. For f(x) = e^x, f(-x) = e^{-x}, which is not equal to e^x except at x = 0.

Even functions mirror across the y-axis, meaning f(-x) = f(x) for every x. A good example is f(x) = x^2. If you replace x with -x, you get (-x)^2 = x^2, which exactly matches f(x). For instance, f(3) = 9 and f(-3) = 9, so the values are the same on both sides of the axis.

The other expressions don’t share this symmetry. For f(x) = x, f(-x) = -x, which isn’t the same as x except at x = 0. For f(x) = sin x, f(-x) = -sin x, again not equal to sin x except at x = 0. For f(x) = e^x, f(-x) = e^{-x}, which is not equal to e^x except at x = 0.