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Mathematics > Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer. 

11-15-2013-MRO_QE_14.png

Which of the following could be the equation of the function graphed in the xy-plane above?

Answer Choices

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Explanation

The function with equation y = ((negative x)^2) + 1 and the function with equation y = absolute value ((x^2) + 1) each have a minimum value of 1 when x = 0, but the function graphed does not have a minimum value of 1, so these options cannot be correct. The graph of the function with equation y = negative (x^2) + 1 contains the point (2 comma negative 3), but the function graphed does not contain any points with negative y-coordinates, so this option cannot be correct. The graph of the function with equation y = absolute value (x minus 1)^2 is not symmetric with respect to the y-axis, so it cannot be the equation of the function graphed. Therefore, the only equation that could correspond to the function graphed is y = absolute value ((x^2) minus 1). Its graph is the absolute value of a parabola opening upward with vertex at (0 comma negative 1).

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