Domain and Range Worksheet



Radical Function Basics, Casio ClassPad 330

Learning Objectives:

• find the value of radicals

• find the domain and range of rational and radical functions

Find the values of radicals:

To find the approximate value of [pic], we need to go to the Main screen and input [pic] or 2^(1/2). Note that by default, the calculator outputs exact values instead of decimals. We can highlight the output and then tap [pic].

It’s a common mistake to use 2^1/2 to try to find the value of [pic]. Think about why. Hint: Order of Operations.

Use your calculator to verify the following result:

[pic] [pic] [pic] [pic] [pic]

Domain and range:

A function’s domain has all possible input (x) values.

A function’s range has all possible output (y) values.

Example 1: [pic]’s domain is (−∞,0)⋃(0, ∞), and it’s range is also (−∞,0)⋃(0, ∞). Graph this function and verify its domain and range.

Example 2: [pic]’s domain is [0, ∞), and it’s range is also [0, ∞). Graph this function to verify its domain and range.

Example 3: [pic]’s domain is (−∞, ∞), and it’s range is also (−∞, ∞). Graph this function to verify its domain and range.

First, figure out each function’s domain and range without using your calculator.

Then, use your calculator to graph the function and double check the domain and range.

Your weapons: Graph&Table, Zoom In, Zoom Out, [pic], [pic], [pic].

|Function |Domain |Range |

|[pic] | | |

|[pic] | | |

|[pic] | | |

|[pic]+1 | | |

|[pic] | | |

|[pic] | | |

|[pic] | | |

|[pic] | | |

|[pic] | | |

|[pic] | | |

|[pic] | | |

|[pic] | | |

|[pic] | | |

|[pic] | | |

|[pic] | | |

|[pic] | | |

|[pic] | | |

Solutions are on the next page.

Solutions:

|Function |Domain |Range |

|[pic] |(−∞, ∞) |(−∞, ∞) |

|[pic] |(−∞, ∞) |[1, ∞) |

|[pic] |(−∞, −1)⋃(−1, ∞) |(−∞, 0)⋃(0, ∞) |

|[pic]+1 |(−∞, 100)⋃(100, ∞) |(−∞, 1)⋃(1, ∞) |

|[pic] |(−∞, −1)⋃(−1, 0)⋃(0, ∞) |(−∞, 0)⋃(0, ∞) |

|[pic] |{x|x∈R, x≠−3, 0, 2} |(−∞, −2)⋃(−2, ∞) |

|[pic] |(−∞, ∞) |(−∞, 0)⋃(0, ∞) |

|[pic] |(−∞, ∞) |[0, ∞) |

|[pic] |[0, ∞) |[0, ∞) |

|[pic] |[−1, ∞) |[0, ∞) |

|[pic] |[1, ∞) |[5, ∞) |

|[pic] |[1, ∞) |(−∞, 5] |

|[pic] |(−∞, 0] |[0, ∞) |

|[pic] |(−1, ∞) |(0, ∞) |

|[pic] |[3, ∞) |[0, ∞) |

|[pic] |(−∞, ∞) |(−∞, ∞) |

|[pic] |(−∞, 0] |(−∞, 1] |

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