# SAT Math Multiple Choice Question 749: Answer and Explanation

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**Question: 749**

**14.**

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).