SAT Math Multiple Choice Question 749: Answer and Explanation
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
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).