PSAT Math Multiple-Choice Question 246: Answer and Explanation

Question: 246

The graph of f(x) passes through the point (5, 1). Through which point does the graph of -f(x + 3) - 2 pass?

• A. (-2, -1)
• B. (2, -3)
• C. (2, 1)
• D. (8, -3)

Correct Answer: B

Explanation:

B

Difficulty: Hard

Category: Passport to Advanced Math/Functions

Getting to the Answer: Transformations that are grouped with the x in a function shift the graph horizontally and, therefore, affect the x-coordinates of points on the graph. Transformations that are not grouped with the x shift the graph vertically and, therefore, affect the y-coordinates of points on the graph. Remember, horizontal shifts are always backward of what they look like. Start with (x + 3). This shifts the graph left 3, so subtract 3 from the x-coordinate of the given point: (5, 1) → (5 - 3, 1) = (2, 1). Next, apply the negative in front of f, which is not grouped with the x, so it makes the y-coordinate negative: (2, 1) → (2, - 1). Finally, - 2 is not grouped with x, so subtract 2 from the y-coordinate: (2, - 1 - 2) → (2, - 3), which is (B).