SAT Math Multiple Choice Question 210: Answer and Explanation

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Question: 210


The graph of f(x) is shown in the xy-plane above. Which of the following could be the graph of - [f(x - 2) + 3] ?

  • A.
  • B.
  • C.
  • D.

Correct Answer: B


BThe line shown has a negative slope. Because the graph transformation asks for the negative value of the transformed function, the resulting graph must have a positive slope. Therefore, eliminate (A). Graph transformation rules state that if the number is within the parentheses, then the graph moves left or right in the opposite direction of the sign, and if the number is outside the parentheses, the graph moves up or down in the same direction of the sign. Therefore, this line will move 2 to the right, and up 3. To follow the proper order of operations, draw out the graph transformation first, and then deal with the negative outside the brackets. Move the line two units to the right to get:

Move the line up 3 to get:

The negative sign outside the brackets means to reflect, or flip, the line over the x-axis. When the line is flipped from a positive to a negative slope, it will still go through point (4, 0). Therefore, the correct answer is (B).

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