Find the maximum and minimum values of the function .

Answer and explanation

Correct answer: C. Maximum = 11, Minimum = 5

  1. Step 1: Recall the fundamental range of the sine function: for all real .
  2. Step 2: Multiply the inequality by , reversing the inequality signs: . Adding 8 across all parts gives . Thus the maximum is 11 and minimum is 5.
Answer
Maximum = 11, Minimum = 5.
Why not the others: Setting maximum = 8 and minimum = -3 neglects the constant offset ; setting maximum = 11 and minimum = 8 considers only positive excursions of the sine term; setting maximum = 8 and minimum = 5 ignores the amplitude multiplier.

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