If f(x) is an even function and the point (x, y) is on the graph of f(x), what other point must be on the graph of f(x)?

Question

GPT-4o mini · Accepted Answer

If $ f(x) $ is an even function and the point $ (x, y) $ is on the graph of $ f(x) $, then by the definition of an even function, it satisfies the property $ f(-x) = f(x) $. Therefore, the point $ (-x, y) $ must also be on the graph of $ f(x) $. In summary, if $ (x, y) $ is on the graph of the even function $ f(x) $, then the point $ (-x, y) $ is also on the graph.