Domain, Range, Intervals, Zeros and Intercepts

Find the domain of the rational function.

• {x|x ≠ -7, x ≠ 7}

• {x|x ≠ -7, x ≠ 7, x ≠ -5}

• all real numbers

• {x|x ≠ 0, x ≠ 49}

Use the graph to determine the domain and range of the function.

• domain: {x|x ≠ 5}

  range: {y|y ≠ 4}

• domain: {x|x ≠ 5}

  range: {y|y ≠ -4}

• domain: {x|x ≠ -4}

  range: {y|y ≠ 5}

• domain: {x|x ≠ 4}

  range: {y|y ≠ 5}

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

• f(1) = 1 and f(2) = -43; yes

• f(1) = -1 and f(2) = -43; no

• f(1) = -1 and f(2) = 43; yes

• f(1) = 1 and f(2) = 43; no

Find all zeros of the function and write the polynomial as a product of linear factors.

• The zeros of the function are x = 1, x = -3, and x = 5. The polynomial can be written as f(x) = (x - 1)(x + 3)(x - 5)

• The zeros of the function are x = 3, x = -5, and x = 2. The polynomial can be written as f(x) = (x - 3)(x + 5)(x - 2)

• The zeros of the function are x = -2, x = -1, and x = 4. The polynomial can be written as f(x) = (x + 2)(x + 1)(x - 4)

• The zeros of the function are x = 1, x = 2, and x = -4. The polynomial can be written as f(x) = (x - 1)(x - 2)(x + 4)

Tags

CCSS.HSF-IF.C.7C

Describe the range of the given function using interval notation.

• (-∞, ∞)

• (-4, 5)

• [-3, 5]

• [-4, 5]

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

What is the range of the given function?

• [-1, 1]

• (-1, 1)

• (∞, -∞)

• (-∞, ∞)

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

Determine the domain and range.

• D: (-∞, ∞); R: (-∞, ∞)

• D: (-3, 3); R: (0, 3)

• D: [-3, 3]; R: [3, 0]

• D: [-3, 3]; R: [0, 3]

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

On which interval(s) is the given function increasing?

• (-∞, 2) U (-2, ∞)

• (-2, 2) U (-2, ∞)

• (-∞, -2) U (0.5, ∞)

• (0, 2) U (0.5, ∞)

Describe the intervals over which the given function is decreasing.

• (-∞, 0) U (2, ∞)

• (5, -4) U (2, -3)

• (-3, 0) U (2, 3)

• (5, -4) U (0, -3)

Write the following in interval notation

-7 ≤ x < 8

• (-7, 8)

• [-7, 8)

• [-7, 8]

• (-7, 8]

Tags

CCSS.6.EE.B.8