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Mathematics>Standard Multiple Choice

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

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

(A) y = ((-x)^2) + 1
(B) y = -(x^2) + 1
(C) y = |((x^2) + 1)|
(D) y = |((x^2)-1)|
(E) y = |(x-1)^2|

答案和解析

答案：D

解析：

The function with equation y = ((-x)^2) + 1 and the function with equation y = |((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 = -(x^2) + 1 contains the point (2，-3), but the function graphed does not contain any points with -y-coordinates, so this option cannot be correct. The graph of the function with equation y = | (x-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 = | ((x^2)-1)|. Its graph is the absolute value of a parabola opening upward with vertex at (0，-1).