PSAT Math Multiple-Choice Question 521: Answer and Explanation

Question: 521

Some values of x and their corresponding f(x) values are shown in the table above. Which of the following functions could represent the relationship between x and f(x)?

• A. f(x) = 4x – 2
• B. f(x) = –2x + 2
• C. f(x) = –3x + 1
• D. f(x) = –4x + 2

Correct Answer: D

Explanation:

D

The question asks for an equation that represents the relationship between two variables. When given a table of values and asked for the correct equation, plug values from the table into the answer choices to see which one works. According to the table, f(x) = 2 when x = 0. Choice (A) becomes 2 = 4(0) – 2, or 2 = –2. This is not true, so eliminate (A). Choice (B) becomes 2 = –2(0) + 2, or 2 = 2. This is true, so keep (B) for now, but check the remaining answers just in case. Choice (C) becomes 2 = –3(0) + 1, or 2 = 1. This is not true, so eliminate (C). Choice (D) becomes 2 = –4(0) +2, or 2 = 2. This is true, so keep (D) for now. Since two answers match the target value, choose a new set of values from the table to plug into the remaining answer choices. According to the table, f(x) = –2 when x = 1. Choice (B) becomes –2 = –2(1) + 2, or –2 = 0. This is not true, so eliminate (B). Choice (D) becomes –2 = –4(1) + 2, or –2 = –2, which is true. The correct answer is (D).