Domain and range of the functions II

​​Domain and range of a function II

By ammar al-qadasi

finding the domain of a function

Multiple Choice

Example 1

• All Real Numbers

• ℝ − {1, -1}

• ℝ − {1}

• ℝ − {0}

finding the domain of a function - Example 1

finding the domain of a function - Example 2

Multiple Choice

Example 2

• All Real Numbers

• ℝ − {0}

• ℝ − {-3, 4}

• ℝ − [-3,4]

finding the domain of a function - Example 2

​ So, the domain of the function is
ℝ − {−3,4} .

Also, the domain is
(−∞,−3) ∪ (−3,4) ∪ (4, ∞) .

Multiple Choice

Example 3

• All Real Numbers

• ℝ − (-2,3)

• ℝ − {-2, 3}

• ℝ − [-2,3]

finding the domain of a function - Example 3

Multiple Choice

Example 4

• All Real Numbers

• ℝ − (-4,4)

• ℝ − {-4, 4}

• [-4,4]

finding the domain of a function - Example 4

​Therefore, the domain is [−4,4].

Multiple Choice

Example 4
Find the range

• All Real Numbers

• [0,4]

• ℝ − {-4, 4}

• [-4,4]

finding the Range of a function - Example 4

Multiple Select

Example 5

• All Real Numbers

• (2,∞)

• ℝ − {-2}

• [-2,∞]

finding the domain of a function - Example 5

Multiple Select

Example 6

• All Real Numbers

• [0,∞)-{4}

• ℝ − {4}

• [-2,∞]

finding the domain of a function - Example 6

Multiple Select

Example 7

• All Real Numbers

• Domain = ℝ − {3}
  Range = ℝ − {3}

• Domain = ℝ − {0}
  Range = ℝ − {3}

• Domain = ℝ − {0}
  Range = ℝ − {0}

finding the domain and Range of a function - Ex 7

Multiple Choice

Example 8

• All Real Numbers

• Domain = ℝ Range = ℝ − {4}

• Domain = ℝ − {0}
  Range = [3,∞)

• Domain = ℝ
  Range = [3,∞)

finding the domain and Range of a function - Ex 8