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Every arm is the exact graph of the equation under it, and the label changes with the pose. A function gives each x exactly one y, so its graph passes the vertical line test: no vertical line meets it twice. Reflection keeps that property. y = f(x) becomes y = -f(x) in the x-axis and y = f(-x) in the y-axis, so x -x, x3 - x x - x and ex e-x, each again a function. The circle x y = 1 is not one: x = 0.6 meets it at y = 0.8 and at y = -0.8. Its two halves, y = ‡/(1 - x), are. #math #maths #functio
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