PSAT Math Multiple-Choice Question 412: Answer and Explanation

Question: 412

If f(x) = x² - x for all x ≤ -1 and f(x) = 0 for all x > -1, which of the following could NOT be a value of f(x)?

• A. -4
• B. 0
• C.
• D. 2

Correct Answer: A

Explanation:

A

Difficulty: Easy

Getting to the Answer: You're looking for a value that is NOT possible for f(x). You're told f(x) = 0 for all x > -1, so you can eliminate (B) right away. The other part of the function gives f(x) = x² - x for all x ≤ -1. Plugging any negative number less than or equal to -1 into this part of the function gives a negative number squared minus the original negative number, which will always be positive. For example, f (-3) = (-3)² - (-3) = 9 + 3 = 12. Therefore, the range of f(x) will always be greater than or equal to 0. This eliminates (C) and (D), leaving (A) as the correct answer.