Graph of a function: Difference between revisions

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Given a mapping <math>f:X \to Y</math>, in other words a function <math>f</math> together with its ___domain <math>X</math> and codomain <math>Y</math>, the graph of the mapping is<ref>{{cite book|author=D. S. Bridges|title=Foundations of Real and Abstract Analysis|url=https://archive.org/details/springer_10.1007-978-0-387-22620-0|year=1991|publisher=Springer|page=285|isbn=0-387-98239-6}}</ref> the set

:<math>G(f)=\{(x,f(x)) \mid x \in X\}</math>,

which is a subset of <math>X\times Y</math>. In the abstract definition of a function, <math>G(f)</math> is actually equal to <math>f</math>.

One can observe that, if, <math>f:\mathbb R^n \to \mathbb R^m </math>, then the graph <math>G(f)

</math> is a subset of of <math>\mathbb R^{n+m}</math> (strictly speaking it is <math>\mathbb R^n \times \mathbb R^m</math>, but one can embed it with the natural isomorphism).

== Examples ==