Editing Graph of a function (section)

=== Functions of one variable ===

[[File:Three-dimensional graph.png|right|thumb|250px|Graph of the [[Function (mathematics)|function]] <math>f(x, y) = \sin\left(x^2\right) \cdot \cos\left(y^2\right).</math>]]

The graph of the function <math>f : \{1,2,3\} \to \{a,b,c,d\}</math> defined by
<math display=block>f(x)=
        \begin{cases}
              a, & \text{if }x=1, \\ d, & \text{if }x=2, \\ c, & \text{if }x=3, 
        \end{cases}
  </math>
is the subset of the set <math>\{1,2,3\} \times \{a,b,c,d\}</math>
<math display=block>G(f) = \{ (1,a), (2,d), (3,c) \}.</math>

From the graph, the domain <math>\{1,2,3\}</math> is recovered as the set of first component of each pair in the graph <math>\{1,2,3\} = \{x :\ \exists y,\text{ such that }(x,y) \in G(f)\}</math>.
Similarly, the [[Range of a function|range]] can be recovered as <math>\{a,c,d\} = \{y : \exists x,\text{ such that }(x,y)\in G(f)\}</math>.
The codomain <math>\{a,b,c,d\}</math>, however, cannot be determined from the graph alone.

The graph of the cubic polynomial on the [[real line]]
<math display=block>f(x) = x^3 - 9x</math>
is
<math display=block>\{ (x, x^3 - 9x) : x \text{ is a real number} \}.</math>

If this set is plotted on a [[Cartesian plane]], the result is a curve (see figure).
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