The graph of f(x) consists of 14 points. six of the points lie in quadrant l of the coordinate plane. if f(x) is an odd function, what is the greatest number of points that can lie in quadrant ll?

1 point.

Step-by-step explanation:

The graph of f(x) consists of 14 points and out of these 6 points lie in quadrant 1. It is given that f(x) is an odd function. An odd function is symmetric about origin. This means the behavior of f(x) would be same in Quadrant 1 and Quadrant 3 and also in Quadrant 2 and Quadrant 4.

So, if 6 of the points lie in Quadrant 1, there must be 6 points in Quadrant 3. Only then then function can be odd.

Out of 14, 12 of the points are in Quadrants 1 and 3, as 6 points are in each of them. The remaining 2 points will be equally/similarly positioned in Quadrant 2 and Quadrant 4. This means there must be 1 point in each of these 2 quadrants, only then f(x) would have similar behavior in these two quadrants and would be termed as odd function.

From all this discussion we can conclude that the greatest number of points that can lie in Quadrant II is 1