SAT Math Multiple Choice Question 911: Answer and Explanation

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Question: 911

11. If g(x) represents a quadratic function, which of the following best describes the relationshipbetween the graphs of g(x) and g(x – 3)?

  • A. The graph of g(x – 3) is 3 units to the left of the graph of g(x).
  • B. The graph of g(x – 3) is 3 units to the right of the graph of g(x).
  • C. The graph of g(x – 3) is 3 units lower than the graph of g(x).
  • D. The graph of g(x – 3) is 3 units higher than the graph of g(x).

Correct Answer: B

Explanation:

B

Difficulty: Easy

Category: Passport to Advanced Math / Functions

Strategic Advice: When working with function notation, transformations that are grouped with the x (here, inside the parentheses) represent horizontal shifts, which are always the opposite of how they appear. For example, the transformation f(x + a) represents a shift to the left while f(x - a) represents a shift to the right.

Getting to the Answer: The - 3 is grouped with the x, so the graph of g(x - 3) is a horizontal shift that is 3 units to the right of the original graph, making (B) correct.

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