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If a = 0 and b = 1, we have f(x) = x^3, which is symmetric about the origin. It's easy to show that f(-x) = -f(x) for all x. If a = 1 and b = 0, we have f(x) = x^2, which is symmetric about the y-axis. It's easy to show that f(-x) = f(x) for all x.
