SAT Math Multiple Choice Question 851: Answer and Explanation

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Question: 851

11. Which of the following scatterplots could be modeled by the equation, where a and b are constants such that a > 1 and x < –1?

  • A.
  • B.
  • C.
  • D.

Correct Answer: B



Difficulty: Hard

Category: Problem Solving and Data Analysis / Scatterplots

Strategic Advice: When matching a scatterplot (or any graph) to an equation, first identify the type of equation present to narrow down the choices.

Getting to the Answer: Because x < -1, the b term in the denominator will have a negative exponent. You can move the b term to the numerator and reverse the sign of its exponent to get y = abx, where a > 1 and x > 1. It is now easier to see that the equation is an exponential equation, which will graph as a curve. This means you can eliminate A and D. Because all the values are now greater than 1, the curve will increase from left to right (gradually at first and then more rapidly), which makes (B) the correct choice.

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