Example  2
“\(y\) is seven times the size of \(x\)” is an example of a written description of a function. Represent this function using a mapping diagram, a table of values, an equation, and a graph for the \(x\)-values \(−3, −2, −1, 0, 1, 2, 3\).

Mapping Diagram

Table of Values

\(x\) (input)
  \(y\) (output)
\((x, y)\)
\(−3\) \(−21\)   \((−3, −21)\)
\(−2\) \(−14\) \((−2, −14) \)
\(−1\) \(−7\) \((−1, −7)\)
\(0\)   \(0\)   \((0, 0) \)
\(1\) \(7\) \((1, 7)\)
\(2\) \(14\) \((2, 14)\)
\(3\) \(21\) \((3, 21)\)

Equation

\(y = 7x \)
Graph

Window Settings
XMin \(−4\)
XMax \(4\)
XScale
\(1\)
YMin \(−25\)
YMax \(25\)
YScale \(5\)


Notice in Example 2 that the written description, mapping diagram, table of values, graph, and equation are different ways of representing the same information. The different representations serve different purposes. For example, an equation is used when algebraic manipulation is required to obtain specific information about the function, while a graph allows you to visualize the relationship between the variables.