PSAT Math Multiple-Choice Question 166: Answer and Explanation

Question: 166

If the function h is defined by h(x) = 2x² - 7x - 3, what is h(x + 3)?

• A. h(x + 3) = 2x² - 7x
• B. h(x + 3) = 2x² - 7x - 6
• C. h(x + 3) = 2x² + 5x - 6
• D. h(x + 3) = 2x² - 23x + 15

Correct Answer: C

Explanation:

C

The question asks for h(x + 3). There are variables in the answer choices, so plug in. Let x = 2. If x = 2, then h(x + 3) = h(2 + 3) = h(5) = 2(5)² - 7(5) - 3 = 2(25) - 35 - 3 = 50 - 38 = 12. Therefore, the target is 12. Plug x = 2 into each choice and eliminate any for which h(5) is not equal to 12. In (A), h(2 + 3) = 2(2²) - 7(2), so h(5) = 2(4) - 14 = 8 - 14 = -6. Eliminate (A). In (B), h(2 + 3) = 2(2²) - 7(2) -6, so h(5) = 2(4) - 14 - 6 = 8 - 20 = -12. Eliminate (B). In (C), h(2 + 3) = 2(2²) + 5(2) - 6, so h(5) = 2(4) + 10 - 6 = 8 + 4 = 12. Keep (C). In (D), h(2 + 3) = 2(2²) - 23(2) + 15, so h(5) = 2(4) - 46 + 15 = 8 - 31 = -23. Eliminate (D). The correct answer is (C).