# SAT Math Multiple Choice Question 598: Answer and Explanation

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**Question: 598**

**13.** 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

Strategic Advice: 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.

Getting to the Answer: 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).