PSAT Math Multiple-Choice Question 98: Answer and Explanation

Question: 98

h(x) = 9 - |x - 3|

In the equation above, h(n) = h(-3). Which of the following could be the value of n?

• A. -6
• B. 3
• C. 9
• D. 12

Correct Answer: C

Explanation:

C

The question asks for the value of n given a function definition. Because the question asks for a specific amount and there are numbers in the answer choices, plug in the answers. In function notation, the number inside the parentheses is the x-value that goes into the function, and the value that comes out of the function is the y-value. Before starting with the answers, find h(-3) because that is what the correct answer will equal. Plug x = -3 into the h function to get h(-3) = 9 -|-3 - 3| = 9 - |-6| = 9 - 6 = 3. The correct answer should give 3 as a value for the function. Start with (B), 3. If n = 3, then h(3) = 9 - |3 - 3| = 9 - |0| = 9. This doesn't match the result for h(-3), so eliminate (B). It may not be clear if a greater or smaller value of n is needed, so just pick another answer choice to try. Try (A). If n = -6, then h(-6) = 9 - |-6 - 3| = 9 - |-9| = 9 - 9 = 0. This doesn't match the value for h(-3), so eliminate (A). Try (C). If n = 9, h(9) = 9 - |9 - 3| = 9 - |6| = 9 - 6 = 3. This matches the value of h(-3). The correct answer is (C).