SAT Math Multiple Choice Practice Question 431: Answer and Explanation

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Question: 431

14. Rock climbing routes are rated on a numbered scale with the highest number representing the most difficult route. Sally tried a range of shoe sizes on each of several routes of varying difficulty and found that when she wore smaller shoes, she could climb routes of greater difficulty. If D represents the difficulty rating of a route Sally successfully climbed and s represents the size of the shoes she wore on such a route, then which of the following could express D as a function of s ?

A. D(s) = s2
B. D(s) =
C. D(s) = 4s
D. D(s) = s - 3.5
E. D(s) =

Correct Answer: E


E Here's the relationship: The smaller the shoes, the greater the difficulty. This is an inverse relationship. So, look for an inverse function. Only E is an inverse function. If you weren't sure, try plugging in 8 and 10 for the s. The function should yield a greater D for 8 than it does for 10. Only E has D(8) > D(10).

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