SAT Math Multiple Choice Question 732: Answer and Explanation

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Question: 732

12. Let the function f be defined by f(x) = 2 - |x - 4| for all real values of x. What is the greatest value of f?

  • A. -2
  • B. 2
  • C. 4
  • D. 6

Correct Answer: B

Explanation:

B

Algebra (absolute value) MEDIUM

The function f(x) = 2 - |x - 4| reaches its greatest value when the absolute value is minimized. Since absolute values cannot be negative, the least value |x - 4| can have is 0, which it has when x = 4:

f(4) = 2 - |4 - 4| = 2 - 0 = 2

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