Editing Function (mathematics) (section)

=== Graphs and plots ===
{{main|Graph of a function}}
[[File:Motor vehicle deaths in the US.svg|thumb|The function mapping each year to its US motor vehicle death count, shown as a [[line chart]]]]
[[File:Motor vehicle deaths in the US histogram.svg|thumb|The same function, shown as a bar chart]]

Given a function <math>f : X\to Y,</math> its ''graph'' is, formally, the set

<math display="block">G=\{(x,f(x))\mid x\in X\}.</math>

In the frequent case where {{mvar|X}} and {{mvar|Y}} are subsets of the [[real number]]s (or may be identified with such subsets, e.g. [[interval (mathematics)|intervals]]), an element <math>(x,y)\in G</math> may be identified with a point having coordinates {{math|''x'', ''y''}} in a 2-dimensional coordinate system, e.g. the [[Cartesian plane]]. Parts of this may create a [[Plot (graphics)|plot]] that represents (parts of) the function. The use of plots is so ubiquitous that they too are called the ''graph of the function''. Graphic representations of functions are also possible in other coordinate systems. For example, the graph of the [[square function]]

<math display="block">x\mapsto x^2,</math>

consisting of all points with coordinates <math>(x, x^2)</math> for <math>x\in \R,</math> yields, when depicted in Cartesian coordinates, the well known [[parabola]]. If the same quadratic function <math>x\mapsto x^2,</math> with the same formal graph, consisting of pairs of numbers, is plotted instead in [[polar coordinates]] <math>(r,\theta) =(x,x^2),</math> the plot obtained is [[Fermat's spiral]].