PSAT Math Multiple-Choice Question 667: Answer and Explanation

Question: 667

Consider the function f(x) = x² + 2.
What operation could be performed on the right-hand side of the equation to expand the range to include negative values?

• A. Add 5
• B. Add -2
• C. Subtract 3
• D. Subtract 1

Correct Answer: C

Explanation:

(C) This function is a parabola. It opens upward because the coefficient in front of x² is positive. (In this case, the coefficient of x² is 1.) The function has a y-intercept of 2. Therefore, the range is [2, ∞). In order for the range to include negative numbers, the new function either needs to open downward or have a negative y-intercept. In order for it to open downward, you would multiply the right side by a negative number, but this isn't a choice.

The only choice that works is subtracting 3, which would make the y-intercept negative. The y-intercept of the new function would be -1 because 2 - 3 = -1. The range of the new function would be expanded to [-1, ∞).