Let f be a function such that f(x) = f(-x) for all real numbers x. If the point (-2, 4) lies on the graph of y = f(x) in the xy-plane, which of the following points must also lie on the graph of y = f(x)?

This point does not satisfy the property of the function. Since ( f(-2) = 4 ), it cannot be the case that ( f(-2) = -4 ). The point (-2, -4) would imply that the function takes on a different value for ( -2 ), contradicting the definition of an even function.

While this point is relevant for many functions, it does not necessarily follow from the given information. The equation ( f(x) = f(-x) ) does not imply that ( f(0) = 0 ). The function could take any value at 0, and we have no information to conclude that (0, 0) must be on the graph.

Similar to choice B, the function might or might not equal 4 when ( x = 0 ). The evenness of the function does not dictate the specific value at ( x = 0). Therefore, we cannot conclude that (0, 4) is a point on the graph.

This point also contradicts the property of the function. If ( f(2) = -4 ), then ( f(-2) ) would need to equal -4, which is inconsistent with the known point (-2, 4). As an even function, ( f(-2) ) must equal 4, ruling out (2, -4).