**Example 1:** Graph

**f( x ) = **^{3}√ (x)

and find the range of f.
**Solution to Example 1:**

Because the domain of f is the set of all real numbers, we might construct a table of values as follows:

**x** | -8 | 1 | 0 | 1 | 8 |

**f(x) = **^{3}√ ( x ) | -2 | 1 | 0 |
1 |
2 |

The values of x were selected so that the cube root of these values are whole numbers which make it easy to plot the points shown in the table.

The range of f is given by the interval (-infinity , +infinity).

**Example 2:** Graph

**f( x ) = **^{3}√ (x - 2)

and find the range of f.
**Solution to Example 2:**

The domain of the cube root function given above is the set of all real numbers.

It easy to calculate ^{3}√ (x - 2)if you select values of (x - 2) as -8, -1, 0, 1 and 8 to construct a table of values then find x in order to graph f.

**x - 2** | -8 | -1 | 0 | 1 | 8 |

**f(x) = **^{3}√ (x - 2) | -2 | -1 | 0 |
1 | 2 |

**x** | -6 | 1 | 2 | 3 | 10 |

Only the last two lines in the table are used to graph f.

The range of f is the set of all real numbers.

Note also that the graph of f(x) = ^{3}√ (x - 2) is that of f(x) = ^{3}√ ( x ) shifted 2 units to the right.

**Example 3:** Graph

**f( x ) = - **^{3}√(x + 1)

and find the range of f.
**Solution to Example 3:**

The domain of the function given above is the set of all real numbers

We now select values of (x + 1) as -8, -1, 0, 1 and 8 to construct a table of values then find x in order to graph f .

**x + 1** | -8 | -1 | 0 | 1 | 8 |

**f(x) = - **^{3}√ (x + 1) | 2 | 1 | 0 |
- 1 | - 2 |

**x** | -9 | -2 | -1 | 0 | 7 |

The range of f is given by the interval (-infinity , +infinity).

**Example 4:** Graph

**f( x ) = - 2 **^{3}√ (x - 2) + 2

and find the range of f.
**Solution to Example 4:**

The domain of function f is the set of all real values.

We now select values of (x - 2) as -8, -1, 0, 1 and 8 to construct a table of values.

**x - 2** | -8 | -1 | 0 | 1 | 8 |

**f(x) = - 2 **^{3}√ (x - 2) + 2 | 6 | 4 | 2 |
0 | - 2 |

**x** | -6 | 1 | 2 | 3 | 10 |

The range of f is the set of all real numbers.

More references and links on graphing.
Graphing Functions