PSAT Math Grid-Ins Question 15: Answer and Explanation

Question: 15

In the above graph, parabola f(x) is represented by the equation f(x) = x² - 4 and line g(x) is represented by the equation g(x)= -x -4. Line g(x) intersects parabola f(x) at point (0, -4).

For x = 12, how much greater is the value of f(x) than g(x)?

Correct Answer: 148

Explanation:

148

The question asks for a comparison between the values of two different functions. In function notation, the number inside the parentheses is the x-value that goes into the function, and the value that comes out of the function is the y-value. Since the question asks for the values of each function when x = 12, it asks for the y-values of each function at this point. First, plug x = 12 into the f function to get f(12) = 12² - 4 = 144 - 4 = 140. Now plug x = 12 into the g function to get g(12) = (12) - 4 = -4 - 4 = -8. At x = 12, f(x) is 140 - (-8) = 148 greater than g(x). The correct answer is 148.