#### Example 7.21.

Graph the cubic polynomial \(P(x) = x^3 - 4x\) and compare its graph with that of the basic cubic, \(y = x^3\text{.}\)

## Solution.

The graph of the basic cubic is shown in figure (a) below. To help us understand the graph of the polynomial \(P(x) = x^3 - 4x\text{,}\) we will evaluate the function to make a table of values. We can do this by hand or use the Table feature on the graphing calculator.

\(x\) | \(-3\) | \(-2\) | \(-1\) | \(0\) | \(1\) | \(2\) | \(3\) |

\(P(x)\) | \(-15\) | \(0\) | \(3\) | \(0\) | \(-3\) | \(0\) | \(15\) |

The graph of \(P(x) = x^3 - 4x\) is shown in figure (b). It is not exactly the same shape as the basic cubic—it has two turning points—but it is similar, especially at the edges of the graphs.