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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?

Respuesta :

f(−x)=−f(x) is an odd function
 All points in Q1 would only be reflected in Q3, and not reflected in quadrant 2 or 4.
So according to above explanation , it wil show six points in quadrant 1 and six in quadrant 3

Answer

As, function is an odd function , it means

f(-x)= -f(x)

So, if you will draw the graph of any of the odd function, if six points lie in first quadrant, similar number of points will be in third Quadrant, as the two parts will be mirror images of each other.

The other two point will be , one is origin (0,0) and other will be a point on X axis.

You can check this ,by taking any of the polynomial function, for example ,x, x³, x+x³, etc.

So, number of points in second quadrant=0

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