Mathematics > Standard Multiple Choice
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 ,-9), (1 ,-4), and (3 ,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 ,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.
The correct answer is D
Explanation
If the graph of the function 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 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 = - (x minus 3)^2, then the graph of function f would contain the points (0 , - 9), (1 , - 4), and (3 , 0). The graph of function f would be a parabola symmetric with respect to the line with equation x = 3. The maximum value of function f would occur at the point (3 , 0), and y less than or equal to 0 would be true for all points (x , y) on the graph of function f.