Answer: The correct option is C.
Explanation:
A function is called an odd function if,
![f(-x)=-f(x)](https://tex.z-dn.net/?f=f%28-x%29%3D-f%28x%29)
It means if the points are in the form of (x,y) then (-x,-y) is also in the graph.
Reason for correct option:
In option C, a point (1,2),
It means,
![f(1)=2](https://tex.z-dn.net/?f=f%281%29%3D2)
And we have another point (-1,-2).
![f(-1)=-f(1)=-2](https://tex.z-dn.net/?f=f%28-1%29%3D-f%281%29%3D-2)
The other points are (2,3),(-2,-3),(3,-1),(-3,1),(4,0),(-4,0). Therefore the function is an odd function.
Reason for incorrect option:
In option A, a point is (1,3), therefore the value of function at x = -1 should be -3.
But the value of function is 1 at x=-1, therefore it is not an odd function.
In option B, a point is (1,0), therefore the value of function at x = -1 should be 0.
But the value of function is -3 at x=-1, therefore it is not an odd function.
In option D, a point is (1,-1), therefore the value of function at x = -1 should be 1.
But the value of function is -1 at x=-1, therefore it is not an odd function.