SAT Math Multiple Choice Question 536: Answer and Explanation
11. If the graph of the function g(x) passes through the point (8, –3), then through which point does the graph of –g(x – 4) – 6 pass?
- A. (–12, –9)
- B. (–12, –3)
- C. (4, –3)
- D. (12, –3)
Correct Answer: D
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: Perform each transformation on the coordinates of the point, one at a time, following the same order of operations that you use when simplifying arithmetic expressions. Start with (x – 4). This shifts the graph right 4 units, so add 4 to the x-coordinate of the given point: (8, –3) → (8 + 4, –3) = (12, –3). Next, apply the negative in front of g, which is not grouped with the x, so it makes the y-coordinate the opposite of what it was: (12, –3) → (12, 3). Finally, the – 6 is not grouped with x, so subtract 6 from the y-coordinate: (12, 3) → (12, 3 – 6) = (12, –3). Therefore, (D) is correct. You could also plot the point on a coordinate plane, perform the transformations (right 4, reflect vertically over the x-axis, and then down 6), and find the resulting point.