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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 comma negative 9), (1 comma negative 4), and (3 comma 0), which of the following CANNOT be true?

Answer Choices

Right! (Applause.)

Explanation

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 (0 comma negative 9) and (1 comma negative 4) would be the same as the slope of the segment connecting the points (1 comma negative 4) and (3 comma 0). However, the slope of the segment connecting the points (0 comma negative 9) and (1 comma negative 4) is 5, and the slope of the segment connecting the points (1 comma negative 4) and (3 comma 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 = negative (x minus 3)^2, then the graph of function f would contain the points (0 comma negative 9), (1 comma negative 4), and (3 comma 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 comma 0), and y less than or equal to 0 would be true for all points (x comma y) on the graph of function f.

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