【SAT每日一题】2013年5月4日SAT官方每日一题

2013-05-06 12:40:00 来源: SAT 责编：楷维留学指南

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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 x y -plane contains the points (0 comma negative 9) , (1 comma negative 4) , and (3 comma 0) , which of the following CANNOT be true?

A. The graph of function f has a maximum value.

B. y less than or equal to 0 for all points (x comma y) on the graph of function f .

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

D. The graph of function f is a line.

E. The graph of function f is a parabola.

正确答案:D

解析:

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

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