function: Quick Facts

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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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Topics

objective function algebraic function continuous function differentiable function probability mass function rational function computable function functor potential function argument foundations of mathematics probability and statistics numerals and numeral systems matrix fractal graph derivative algorithm vector error

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analysis: Functions

Key People

Paul Painlevé.

Paul Painlevé

French prime minister and mathematician

Karl Weierstrass

Karl Weierstrass

German mathematician

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Émile Borel

French mathematician

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Edward Charles Titchmarsh

British mathematician

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Peter Gustav Lejeune Dirichlet

German mathematician

Italian-born physicist Dr. Enrico Fermi draws a diagram at a blackboard with mathematical equations. circa 1950.

Define It: Math Terms

Equations written on blackboard

Numbers and Mathematics