Question

the zeroes of the function are -2, 0, and 4.
none of the zeroes have a multiplicity of 2.
what intervals would you use to determine where the function is positive and negative?
\\((-2, 4)\\)
\\((-\infty, -2), (-2, 0), (0, 4), \text{ and } (4, \infty)\\)
\\((-\infty, -2), (-2, 4), \text{ and } (4, \infty)\\)
\\((-\infty, \infty)\\)

Explanation:

Identify the zeroes of the function

$$ x = -2, \quad x = 0, \quad x = 4 $$

Determine the partition intervals

$$ (-\infty, -2), \quad (-2, 0), \quad (0, 4), \quad (4, \infty) $$

Answer:

• (A) \((-2, 4)\)
• (B) \((-\infty,-2)\), \((-2, 0)\), \((0, 4)\), and \((4, \infty)\) (Correct answer)
• (C) \((-\infty,-2)\), \((-2, 4)\), and \((4, \infty)\)
• (D) \((-\infty,\infty)\)