PSAT Math Multiple-Choice Question 136: Answer and Explanation

Question: 136

The graphs of the functions g and h are shown above. Which of the following defines h in terms of g?

• A. h(x) = -g(x)
• B. h(x) = |g(x)|
• C. h(x) = g(x) + 3
• D. h(x) = g(x - 3)

Correct Answer: B

Explanation:

B

The question asks for the equation of h(x) in terms of g(x). The graph of h(x) is the same as the graph of g(x) at every point where y is greater than or equal to 0, but for all the points where y is less than 0 on the graph of g(x), the graph is flipped from below the x-axis to above it on the graph of h(x). The transformation that would cause this would be absolute value, which is (B). Choice (A) would flip all values of g(x) over the x-axis, but only the negative y-values were flipped. Choice (C) would shift g(x) up three units, but the positive values are not shifted, and the negative values are reflected. Choice (D) would shift g(x) to the right three units, but once again the positive values aren't shifted. The correct answer is (B).