出国留学首选一诺留学

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

　　If the graph of the function function f in the xy -plane contains the points (0, -9), (1, -4) , and (3, 0) , which of the following CANNOT be true?

　　(A) The graph of f has a maximum value.

　　(B) y ≤0 for all points (x, y) on the graph of f .

　　(C) The graph of f is symmetric with respect to a line.

　　(D) The graph of f is a line.

　　(E) The graph of f is a parabola.

　　The correct answer is D

　　Explanation

　　If the graph of the function f , which contains the points (0, -9), (1, -4), and (3, 0) , were a line, then the slope of the segment connecting the points (0, -9) and (1, -4) would be the same as the slope of the segment connecting the points (1, -4) and (3, 0) . However, the slope of the segment connecting the points (0, -9) and (1, -4) is 5 , and the slope of the segment connecting the points (1, -4) and (3, 0) is 2 . Therefore, the graph of f cannot be a line.

　　The statements in the other four options could be true. For example, if the equation of f were y =- (x-3) 2 , then the graph of f would contain the points (0, -9), (1, -4), and (3, 0) . The graph of f would be a parabola symmetric with respect to the line with equation x = 3 . The maximum value of f would occur at the point (3, 0) , and y ≤0 would be true for all points (x, y) on the graph of f .

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