PSAT Math Multiple-Choice Question 769: Answer and Explanation

Question: 769

The function f is given by f(x) = 2 – |x – 4|. For what value of x does the function f achieve its maximum value?

• A. 2
• B. 4
• C. 5
• D. 6

Correct Answer: B

Explanation:

(B) Notice that the function is 2 minus the absolute value of something. The absolute value of something must always be greater than or equal to 0. So either f(x) = 2 - 0 = 2 or f(x) equals 2 minus some positive number. This second case, though, will result in a value that is less than 2. (Convince yourself of this. For instance, if the absolute value is 1, then f(x) = 2 - 1 = 1.) Therefore, the maximum value of f is 2. To find where this maximum will occur, we need to determine which x-values give |x - 4| = 0. This occurs when x - 4 = 0 . Thus, x = 4, which is choice (B).
Alternatively, you could have plugged in the potential x-values to determine which gives the maximum value for f(x).