SAT Math Multiple Choice Question 334: Answer and Explanation

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Question: 334

4.

A start-up business is typically one that offers a "new" type of service or produces a "new" product. Start-ups are designed to search for a sustainable business model. The function shown in the graph represents new business start-up rates in the United States from 1977 to 2013 as reported by the U.S. Census Bureau. If t represents the year, then which of the following statements correctly describes the function?

  • A. The function is increasing overall.
  • B. The function is decreasing overall.
  • C. The function is increasing for all t such that 1977 < t < 2013.
  • D. The function is decreasing for all t such that 1977 < t < 2013.

Correct Answer: B

Explanation:

B

Difficulty: Easy

Category: Passport to Advanced Math / Functions

Strategic Advice: Your only choice for this question is to compare each statement to the graph. Cross out false statements as you go. Pay attention to keywords that tell you whether the statement is a general statement or a precise statement.

Getting to the Answer: A function is decreasing when the slope is negative; it is increasing when the slope is positive. You can see from the graph that the trend is decreasing (going down from left to right), so eliminate A and C. Now, take a closer look to see that there are some time intervals over which the function increases (goes up), so you can't say that the function in decreasing for all t such that 1977 < t < 2013. You can only make a general statement about the nature of the function, like the one in (B). The right-hand side of the graph is lower than the left side, so the function is decreasing overall.

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