Graph of a function: Difference between revisions

Revision as of 16:37, 24 February 2022

Revision as of 17:15, 24 February 2022

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Oftentimes it is helpful to show with the graph, the gradient of the function and several level curves. The level curves can be mapped on the function surface or can be projected on the bottom plane. The second figure shows such a drawing of the graph of the function:

<math display=block>f(x, y) = -(\cos(x^2) + \cos(y^2))^2.</math>

== Generalizations ==

The graph of a function is contained in a [[Cartesian product]] of sets. An <math>X</math>–<math>Y</math> plane is a Cartesian product of two lines, called <math>X</math> and <math>Y,</math> while a cylinder is a cartesian product of a line and a circle, whose height, radius, and angle assign precise locations of the points. [[Fibre bundle]]s are not Cartesian products, but appear to be up close. There is a corresponding notion of a graph on a fibre bundle called a [[Section (fiber bundle)|section]].

The {{visible anchor|graph of a multifunction}}, say the [[Multivalued function|multifunction]] <math>\mathcal{R} : X \rightrightarrows Y,</math> is the set <math>\operatorname{gr} \mathcal{R} := \left\{ (x, y) \in X \times Y : y \in \mathcal{R}(x) \right\}.</math>

== See also ==