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function
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A graph of the function f(x) = x cubed minus 3x plus 2 is shown on a blue background, with a red curve passing through key points. Local maximum and minimum points are marked with black dots at x equals negative 1 and x equals 1, illustrating important features of the curve. Four graphs display the curves of sine, cosine, tangent, and cotangent functions, each labeled with x- and y-axes, key angles in radians, and typical wave or asymptote patterns. A diagram of the complex plane with horizontal real axis and vertical imaginary axis, showing a point labeled x + iy and dashed lines connecting it to coordinates x on the real axis and y on the imaginary axis. Two panels showing function graphing concepts: Panel A illustrates plotting an arbitrary function f by selecting values of t and marking corresponding f(t) points; Panel B graphs the specific parabola f(t) equals t squared, with plotted points showing how t values map to t squared. Both graphs use dashed lines to connect points to the axes for clarity. Figure 1: Graph of values of the function y = f(x) = 2 - x + x2 for x = 0, 1, 2, 3, and 4.
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Italian-born physicist Dr. Enrico Fermi draws a diagram at a blackboard with mathematical equations. circa 1950.
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A graph of the function f(x) = x cubed minus 3x plus 2 is shown on a blue background, with a red curve passing through key points. Local maximum and minimum points are marked with black dots at x equals negative 1 and x equals 1, illustrating important features of the curve.
cubic equation Plot of the cubic equation f(x) = x3 − 3x + 2. The plotted points are where changes in curvature occur.

function

mathematics
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function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are ubiquitous in mathematics and are essential for formulating physical relationships in the sciences. The modern definition of function was first given in 1837 by the German mathematician Peter Dirichlet: This relationship is commonly symbolized as y = f(x)—which is said “f of x”—and y and x are related such...

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