SAT Math Multiple Choice Question 749: Answer and Explanation

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Question: 749

14. Images

The figure above shows the graphs of functions f and g in the xy-plane. Which of the following equations could express the relationship between f and g?

  • A. f(x) = g(x - 2)
  • B. f(x) = g(x + 2)
  • C. f(x) = g(x) + 2
  • D. f(x) = g(x) - 2

Correct Answer: B

Explanation:

B

Advanced Mathematics (function transformations) HARD

The figure clearly shows that the function y = f(x) is similar in shape to the function y = g(x), but is shifted to the left by some positive distance. Recall from Chapter 9, Lesson 3, that when the graph of y = g(x) is shifted to the left by k units, the equation of the new function is y = g(x + k). The only equation that has this form is (B) f(x) = g(x + 2).

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