- Graph of a function
In mathematics, the

**graph**of a function "f" is the collection of allordered pair s ("x", "f"("x")). In particular, if "x" is areal number , "graph" means the graphical representation of this collection, in the form of acurve on a Cartesian plane, together with Cartesian axes, etc. Graphing on a Cartesian plane is sometimes referred to as**curve sketching**. If the function input "x" is an ordered pair ("x"_{1}, "x"_{2}) of real numbers, the graph is the collection of allordered triple s ("x"_{1}, "x"_{2}, "f"("x"_{1}, "x"_{2})), and its graphical representation is asurface (seethree dimensional graph ).The graph of a function on real numbers is identical to the graphic representation of the function. For general functions, the graphic representation cannot be applied and the formal definition of the graph of a function suits the need of mathematical statements, e.g., the

closed graph theorem infunctional analysis .The concept of the graph of a function is generalised to the graph of a relation. Note that although a function is always identified with its graph, they are not the same because it will happen that two functions with different

codomain could have the same graph. For example, the cubic polynomial mentioned below is asurjection if its codomain is thereal number s but it is not if its codomain is the complex field.**Examples****Functions of one variable**The graph of the function: $f(x)=\; left\{egin\{matrix\}\; a,\; mbox\{if\; \}x=1\; \backslash \; d,\; mbox\{if\; \}x=2\; \backslash \; c,\; mbox\{if\; \}x=3.\; end\{matrix\}\; ight.$is:{(1,a), (2,d), (3,c)}.

The graph of the cubic polynomial on the

real line : $f(x)=$x^3}-9x} ! is: {("x", "x"^{3}-9"x") : "x" is a real number}.If this set is plotted on a Cartesian plane, the result is a curve (see figure).**Function of two variables**The graph of the

trigonometric function on the real line: "f(x, y) = sin(x^{2})·cos(y^{2})"is: {("x", "y", sin(x^{2})·cos(y^{2})) : "x" is a real number}.If this set is plotted on a three dimensional Cartesian coordinate system, the result is a surface (see figure).**Tools for plotting function graphs**Hardware *

Graphing calculator

*Oscilloscope Software See

List of graphing software **See also**

* Critical point

*Derivative

* Epigraph

*Chart

*Stationary point

*Slope

*Solution point

*Tetraview

*Vertical translation

*Y-intercept **External links*** [

*http://www.thinkanddone.com/ge/default.html Online Function Graphing with GraphEasy*]

* [*http://web01.shu.edu/projects/reals/classes/tools.html Some Java applets to study Real Functions*]

* Weisstein, Eric W. " [*http://mathworld.wolfram.com/FunctionGraph.html Function Graph*] ." From MathWorld--A Wolfram Web Resource.

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