6.2 Cubic Domain & Range

The graph of a function is shown.  What are the domain and range of this function?

• Domain: (-∞, ∞)
  Range: (-∞, 2]
• Domain: [2, ∞)
  Range: (-∞, ∞)
• Domain: (-∞, ∞)
  Range: (-∞, ∞)
• Domain: (-∞, 2]
  Range: [2, ∞)

What is the range of ALL cubic functions expressed as an inequality?

• [-∞, ∞]
• (-∞,∞)
• -∞≤y≤∞
• -∞<y< ∞

What is the domain of the cubic function?

• Verbal: All real numbers

  Interval: (-∞, ∞)

  Inequality: x∊ℝ

• Verbal: x is all real numbers

  less than or equal to -2

  Interval: (-∞, -2]

  Inequality: x ≤ -2

• Verbal: y is all real numbers

  less than or equal to 2

  Interval: (-∞, 2]

  Inequality: y ≤ 2

What is the range of the cubic function?

• Verbal: All real numbers

  Interval: (-∞, ∞)

  Inequality: y∊ℝ

• Verbal: x is all real numbers

  less than or equal to -2

  Interval: (-∞, -2]

  Inequality: x ≤ -2

• Verbal: y is all real numbers

  less than or equal to 2

  Interval: (-∞, 2]

  Inequality: y ≤ 2

What is the domain of the cubic function?

• Verbal: x is all real numbers greater than or equal to -1 and less than 3

  Interval Notation: [-1, 3)

  Inequality Notation: -1 ≤ x < 3

• Verbal: y is all real numbers greater than or equal to -2 and less than 13

  Interval Notation: [-3, 13)

  Inequality Notation: -3 ≤ y < 13

• Verbal: All real numbers

  Interval Notation: (-∞, ∞)

  Inequality Notation: x∈ℝ

• Verbal: x is all real numbers greater than or equal to -2 and less than 13

  Interval Notation: [-3, 13)

  Inequality Notation: -3 ≤ x < 13

What is the range of the cubic function?

• Verbal: x is all real numbers greater than or equal to -1 and less than 3

  Interval Notation: [-1, 3)

  Inequality Notation: -1 ≤ x < 3

• Verbal: y is all real numbers greater than or equal to -2 and less than 13

  Interval Notation: [-3, 13)

  Inequality Notation: -3 ≤ y < 13

• Verbal: All real numbers

  Interval Notation: (-∞, ∞)

  Inequality Notation: x∈ℝ

• Verbal: y is all real numbers greater than or equal to -1 and less than 3

  Interval Notation: [-1, 3)

  Inequality Notation: -1 ≤ y < 3

A refrigerator has a width of (x), a depth of (2x), and a height of (3x + 2). What is the domain and range of the function for this situation?

• Domain: All real numbers greater than 0.

  Range: All real numbers greater than 0.

• Domain:

  (0, 0.5)∪(1, ∞)

  Range:

  (0, ∞)

• Domain: All real numbers greater than or equal to 8.

  Range: All real numbers greater than or equal to 208.

• Domain: 0 < x ≤ 15

  Range: 0 < y ≤ 5700

A wrapped gift box has a width of (x – 1), a length of (2x – 1), and a height of (x). What is the domain and range of the function for this situation?

• Domain: All real numbers greater than 0.

  Range: All real numbers greater than 0.

• Domain:

  (0, 0.5)∪(1, ∞)

  Range:

  (0, ∞)

• Domain: All real numbers greater than or equal to 8.

  Range: All real numbers greater than or equal to 208.

• Domain: 0 < x ≤ 15

  Range: 0 < y ≤ 5700

A building brick has a height of (x), a width of (-x + 25), and a length of (x + 23). The maximum volume of the brick is 5700 cubic units. What is the domain and range for this situation?

• Domain: All real numbers greater than 0.

  Range: All real numbers greater than 0.

• Domain: (0, 0.5)∪(1, ∞)

  Range: (0, ∞)

• Domain: All real numbers greater than or equal to 8.

  Range: All real numbers greater than or equal to 208.

• Domain: 0 < x ≤ 25

  Range: 0 < y ≤ 5700

What is the RESTRICTED domain and range?

• Domain: All real numbers

  Range: All real numbers

• Domain: (-∞, ∞)

  Range: (-∞, ∞)

• Domain: [-3, 2]

  Range: [-8, 4]

• Domain: ℝ

  Range: y>0