PSAT Math Multiple-Choice Question 94: Answer and Explanation

Question: 94

The function f is shown in the xy-plane above. Which of the following could be f(x)?

• A. f(x) = x(x + 2)
• B. f(x) = x(x - 2)
• C. f(x) = x(x + 2)²
• D. f(x) = x(x - 2)²

Correct Answer: D

Explanation:

D

The question asks for an equation that represents a graph. To find the best equation, plug points from the graph into the equations in the answer choices. It's easiest to start with zeroes, but plugging in the origin often makes more than one equation work. Instead, start with (2, 0). In function notation, f(x) = y. Make x = 2 and f(x) = 0 in each answer choice and eliminate any choice that is not true. Choice (A) becomes 0 = (2)(2 + 2), or 0 = (2)(4), which is 0 = 8. Eliminate (A). Choice (B) becomes 0 = (2)(2 - 2), which is 0 = (2)(0) or 0 = 0. Keep (B) but check the remaining answers just in case. Choice (C) becomes 0 = (2)(2 + 2)², which is 0 = (2)(4)² or 0 = 32. Eliminate (C). Choice (D) becomes 0 = (2)(2 - 2)², which is 0 = (2)(0)² or 0 = 0. Keep (D). Next, plug in another point. It is hard to tell exactly where the line hits when x = 1, but it is positive between x = 0 and x = 2. When x = 1, (B) becomes f(1) = (1)(1 - 2) = (1)(-1) = -1 and (D) becomes f(1) = (1)(1 - 2)² = (1)(-1)² = 1. The value of f(1) should be positive, so eliminate (B). The correct answer is (D).