PSAT Math Multiple-Choice Question 418: Answer and Explanation

Question: 418

The graph of f(x) is shown above. Which of the following represents the domain and range of the function?

• A. Domain: f(x) ≥ 5
  Range: all real numbers
• B. Domain: f(x) ≤ 5
  Range: all real numbers
• C. Domain: all real numbers
  Range: f(x) ≥ 5
• D. Domain: all real numbers
  Range: f(x) ≤ 5

Correct Answer: D

Explanation:

D

Difficulty: Easy

Getting to the Answer: To determine the domain, look at the x-values. To determine the range, look at the y-values. For the domain, the graph is continuous and has arrows on both sides, so the domain is all real numbers. This means you can eliminate choices (A) and (B). For the range, the function's maximum is located at (0, 5), which means the highest possible value of f(x) is 5. The graph is continuous and opens downward, so the range of the function is f(x) ≤ 5, making (D) correct.