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The Monotonicity of a function mean usually then a function is strictly increasing, strictly decreasing or constant. Function strictly increasing. The Definition of a strictly increasing function: For every x_1 * x_2: f(x_1) * f(x_2). Function strictly decreasing. The Definition of a strictly decreasing function. For every x_1 * x_2: f(x_1) * f(x_2). Function constant. The Definition of a constant function: For every x: f(x) = c.