Graph of a function: Difference between revisions

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[[File:Polynomial of degree three.svg|thumb|250x250px|Graph of the function <math>f(x)=\frac{x^3+3x^2-6x-8}{4}.</math>]]

In [[mathematics]], the '''graph''' of a [[Function (mathematics)|function]] <math>f</math> is the set of [[ordered pair]]s <math>(x, y)</math>, where <math>f(x) = y.</math> In the common case where <math>x</math> and <math>f(x)</math> are [[real number]]snumbers, these pairs are [[Cartesian coordinates]] of points in [[two-dimensional space]] and thus form a subset of this plane.

In the case of functions of two variables, that is functions whose [[Domain of a function|___domain]] consists of pairs <math>(x, y),</math> the graph usually refers to the set of [[ordered triple]]s <math>(x, y, z)</math> where <math>f(x,y) = z,</math> instead of the pairs <math>((x, y), z)</math> as in the definition above. This set is a subset of [[three-dimensional space]]; for a continuous [[real-valued function]] of two real variables, it is a [[Surface (mathematics)|surface]].