Question

Which graph represents an odd function?

Answer 1

Answer:

The first graph in the second image is an odd function.

Step-by-step explanation:

An odd function has a graph that it's symmetric about the origin, that is, the origin is like a mirror. In other words, the graph of an odd function has a specific symmetry about the origin.

So, we have to look for those graph that has symmetrical points in opposite quadrants, I and III or II and IV.

You can observe that the first graph of the second image has this behaviour. You can see that the points are symmetrical across the origin. If you graph a line defined as y=-x, you will observe that such line acts like a mirror.

Therefore, the odd function is the first graph in the second image.

Answer 2

Answer:

The second graph represents an odd function.

Step-by-step explanation:

For a function f to be odd, it should satisfy the following equation:

f(-x) = -f(x)

The graph of an odd function will always be symmetric about the origin.

By observing the graphs we can say that:

• 1st graph is symmetric about y-axis.Hence it is not an odd function.
• 2nd graph is symmetric about origin and hence it is an odd function.
• 3rd and 4th graph do not have any symmetries.

Hence 2nd graph represents an odd function.