Graph (Function)

Technically, the graph of a function is its Range (a.k.a. image). Informally, given a Function $f(x_1, \ldots, x_n)$ defined on a Domain $U$, the graph of $f$ is defined as a Curve or Surface showing the values taken by $f$ over $U$ (or some portion of $U$),

$$\mathop{\rm graph} f(x) \equiv \{(x,F(x))\in\Bbb{R}^2: x\in U\}$$

$$\mathop{\rm graph} f(x_1,\ldots ,x_n) \equiv \{ (x_1,\ldots ... ..._1,\ldots ,x_n)) \in \Bbb{R}^{n+1}: (x_1,\ldots ,x_n) \in U\}.$$

A graph is sometimes also called a Plot.

Good routines for plotting graphs use adaptive algorithms which plot more points in regions where the function varies most rapidly (Wagon 1991, Math Works 1992, Heck 1993, Wickham-Jones 1994).

See also Curve, Extremum, Graph (Graph Theory), Histogram, Maximum, Minimum

References

Graphing

Cleveland, W. S. The Elements of Graphing Data, rev. ed. Summit, NJ: Hobart, 1994.

Heck, A. Introduction to Maple, 2nd ed. New York: Springer-Verlag, pp. 303-304, 1993.

Math Works. Matlab Reference Guide. Natick, MA: The Math Works, p. 216, 1992.

Tufte, E. R. The Visual Display of Quantitative Information. Cheshire, CN: Graphics Press, 1983.

Tufte, E. R. Envisioning Information. Cheshire, CN: Graphics Press, 1990.

Wagon, S. Mathematica in Action. New York: W. H. Freeman, pp. 24-25, 1991.

Wickham-Jones, T. Computer Graphics with Mathematica. Santa Clara, CA: TELOS, pp. 579-584, 1994.

Yates, R. C. ``Sketching.'' A Handbook on Curves and Their Properties. Ann Arbor, MI: J. W. Edwards, pp. 188-205, 1952.