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A '''two-dimensional graph''' may refer to
{{unreferenced|date=April 2018}}
* The [[graph of a function]] of one variable
A '''two-dimensional graph''' is a set of points in [[two-dimensional space]]. If the points are [[Function of a real variable|real]] and if [[Cartesian coordinates]] are used, each [[axis (mathematics)|axis]] depicts the potential values of a particular [[real number|real variable]]. Often the variable on the horizontal axis is called ''x'' and the one on the vertical axis is called ''y'', in which case the horizontal and vertical axes are sometimes called the ''x'' axis and ''y'' axis respectively. With real variables on the axes, each point in the [[graph of a function|graph]] depicts the values of two real variables.
* A [[planar graph]]
* A [[diagram]] in a plane
{{mathdab}}
Alternatively, each point in a graph may depict the value of a single [[complex variable]]. In this case, the horizontal axis is called the real axis and depicts the potential values of the real part of the [[complex number]], while the vertical axis is called the [[imaginary number|imaginary]] axis and depicts the potential values of the imaginary part of the complex number.
[[Image:cubicpoly.svg|right|thumb|400 px| Graph of the function <math>f(x)={{x^3}-9x} \!\ </math>]]
==Graph of a function==
{{Main|Graph of a function}}
If the relation between the two real variables is of the form <math>y=f(x)</math> where ''f'' is a [[Function (mathematics)|function]] giving a single value of ''y'' associated with each admissible value of ''x'', then the graph is called the graph of a function. The function could be a [[polynomial]] function or a [[transcendental function]].
For example, the graph of the [[cubic polynomial]]
: <math>f(x)={{x^3}-9x} \!\ </math>
is
: {(''x'', ''x''<sup>3</sup>−9''x'') : ''x'' is a real number}.
If this set is plotted on a [[Cartesian plane]], the result is a curve (see figure).
==Graph of a non-function relation==
[[Image:Circle center a b radius r.svg|thumb|right|Circle of radius ''r'' = 1, centre (''a'', ''b'') = (1.2, −0.5)]]
{{see also|Binary relation|Plane curve}}
In some cases the relation between two real variables cannot be written in the form <math>y=f(x)</math>. In other words, it is not a function. Nevertheless, the set of all points given by the relation is still a two-dimensional graph, as in the accompanying graph of the circle <math>(x-a)^2+(y-b)^2=1.</math>
An [[image (mathematics)|image]] of a [[plane curve]] is also a two-dimensional graph, although only some two-dimensional graphs are an image of any plane curve.
==Superimposed graphs of more than one function==
[[File:Supply-and-demand.svg|thumb|left|240px|The price P of a product is determined by a balance between production at each price (supply S) and the desires of those with [[purchasing power]] at each price (demand D). The diagram shows a positive shift in demand from D<sub>1</sub> to D<sub>2</sub>, resulting in an increase in price (P) and quantity sold (Q) of the product.]]
In some contexts it is useful to graph two or more functions together in the same diagram. An example is the [[supply and demand]] graph commonly used in [[Economic graph|economics]], shown here.
== Graph of geometric shapes ==
[[File:Area.svg|thumb|250px|Geometric shapes in 2 dimensions]]
Two-dimensional [[geometric shape]]s are sets of points bounded by [[line segment]]s or [[curve]]s, so a shape can also be constructed by graphs of several equations of its boundary. [[Polygon]]s are the shapes that are only bounded by line segments. These can be visualized by using two-dimensional graphs. Graphs of two polygons, a [[parallelogram]] and a [[right triangle]], are shown here along with the graph of a circle.
==See also==
*[[Graph (disambiguation)]]
*[[Graph of a function of two variables|Three-dimensional graph]]
*[[List of two-dimensional geometric shapes]]
*[[Analytic geometry]]
*[[Cartesian coordinate system]]
*[[Euclidean space]]
*[[Coordinate system]]
*[[Dimension]]
[[Category:Charts]]
[[Category:Functions and mappings]]
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