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Mathematics > Standard Multiple Choice

If the graph of the function in the -plane contains the points , , and , which of the following CANNOT be true?

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### Explanation

If the graph of the function , which contains the points , , and , 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 and is . Therefore, the graph of cannot be a line.

The statements in the other four options could be true. For example, if the equation of were , then the graph of would contain the points , , and . The graph of would be a parabola symmetric with respect to the line with equation . The maximum value of would occur at the point , and would be true for all points on the graph of .