Domain and Range Worksheet



Mrs.Volynskaya Precalculus Honors 9/12 Class Work Name___________________

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.

|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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