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cubic equation graphs of some trigonometric functions point in the complex plane Graph of a functionPart A illustrates the general idea of graphing any function: choose a value for the independent variable, t, calculate the corresponding value for f(t), and repeat this process until the general shape of the graph is apparent. (In practice, various techniques are available to reduce the number of values needed to determine the graph's basic shape.) In part B a specific function, the parabola f(t) = t2, is graphed for further illustration. 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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Photos

cubic equation
graphs of some trigonometric functions
point in the complex plane
Graph of a functionPart A illustrates the general idea of graphing any function: choose a value for the independent variable, t, calculate the corresponding value for f(t), and repeat this process until the general shape of the graph is apparent. (In practice, various techniques are available to reduce the number of values needed to determine the graph's basic shape.) In part B a specific function, the parabola f(t) = t2, is graphed for further illustration.
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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Key People

Paul Painlevé.
Paul Painlevé
French prime minister and mathematician
Karl Weierstrass, engraving after a photograph by Franz Kullrich.
Karl Weierstrass
German mathematician
Émile Borel
French mathematician
Edward Charles Titchmarsh
British mathematician
Peter Gustav Lejeune Dirichlet
German mathematician

Related Quizzes and Features

Quiz
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