Question

I have some graphs, and I need to determine which one is an odd function.

Answer 1

Note that an odd function is :

$-f(x)=f(-x)$

It means that for example, in a function f(x), the point is (x, y)

the other point (-x, -y) must exist.

If a point is (2, 4), the other point must be (-2, -4)

From the given graphs, the third graph satisfies this condition.

One point is (1, 2), so the other point must be (-1, -2). And this point exists in the graph.

Another point is (3, -1), so the other point must be (-3, 1). And this point also exists in the graph.

The remaining points will satisfy just like the previous two above.

So the answer is the graph in the image shown above.