The graph of f(x) consists of 14 points. Six of the points lie in Quadrant I of the coordinate plane. If f(x) is an odd function, what is the greatest number of points that can lie in Quadrant II?

For an odd function, every point (x, y) is paired with the point (−x, −y). So the six points in Quadrant I require six matching points in Quadrant III, using 12 of the 14 points. Any point in Quadrant II must be paired with a point in Quadrant IV, so the two remaining points can make at most one such pair. The greatest number in Quadrant II is one, choice A.

AI-written and checked against the verified answer.