PSAT Math Multiple-Choice Question 514: Answer and Explanation

Question: 514

The table below displays coordinate pairs of a function.

Of the equations listed, which of the following correctly displays the relationship between the values of x and f(x) in the table?

• A. f(x) = –5x
• B. f(x) = –4x + 2
• C. f(x) = –2x – 4
• D. f(x) = 2x + 2

Correct Answer: B

Explanation:

B

The question asks for 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) = 10 when x = –2. Choice (A) becomes 10 = –5(–2), which simplifies to 10 = 10. This is true, so keep (A) but check the remaining answer choices just in case. Choice (B) becomes 10 = –4(–2) + 2 or 10 = 8 + 2. This is also true, so keep (B). Choice (C) becomes 10 = –2(–2) – 4 or 10 = 4 – 4. This is not true, so eliminate (C). Choice (D) becomes 10 = 2(–2) + 2 or 10 = –4 + 2. This is not true, so eliminate (D). Since there are two answer choices remaining, plug in another point. According to the table, f(x) = 6 when x = –1. Choice (A) becomes 6 = –5(–1) or 6 = 5. This is not true, so eliminate (A). Choice (B) becomes 6 = –4(–1) + 2 or 6 = 4 + 2. This is true, so keep (B). The correct answer is (B).