section_path: Representing a function/Graphs and plots
section_name: Graphs and plots
paragraph_text: Graphs and plots
  
  Given a function f: X → Y, {\displaystyle f:X\to Y,} its graph is, formally, the set
  
  In the frequent case where X and Y are subsets of the real numbers (or may be identified with such subsets, e.g. intervals), an element (x, y) ∈ G {\displaystyle (x,y)\in G} may be identified with a point having coordinates x, y in a 2-dimensional coordinate system, e.g. the Cartesian plane. Parts of this may create a 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
  
  consisting of all points with coordinates (x, x 2) {\displaystyle (x,x^{2})} for x ∈ R, {\displaystyle x\in \mathbb {R},} yields, when depicted in Cartesian coordinates, the well known parabola. If the same quadratic function x ↦ x 2, {\displaystyle x\mapsto x^{2},} with the same formal graph, consisting of pairs of numbers, is plotted instead in polar coordinates (r, θ) = (x, x 2), {\displaystyle (r,\theta)=(x,x^{2}),} the plot obtained is Fermat's spiral.