SAT Math Multiple Choice Question 113: Answer and Explanation

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Question: 113

8. Given the equation y = 3x2 + 4, what is the function of the coefficient of 3 ?

  • A. It moves the graph of y = 3x2 + 4 three units higher than the graph of y = x2 + 4.
  • B. It moves the graph of y = 3x2 + 4 three units lower than the graph of y = x2 + 4.
  • C. It makes the graph of y = 3x2 + 4 wider than the graph of y = x2 + 4.
  • D. It makes the graph of y = 3x2 + 4 narrower than the graph of y = x2 + 4.

Correct Answer: D

Explanation:

D When a function f(x) is transformed into a function of the form f(ax), where a is a constant, if a > 0, the function will be compressed horizontally by a factor of a. Here, y = x2 + 4 can be represented as the parent function, and y = 3x2 + 4 as the transformed function compressed horizontally versus the parent function, and thus narrower, by a factor of 3. This is (D). If you're not sure, try plugging values into each equation to construct a rough graph of each equation and compare them.

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