# How to tell if a graph is even or odd or neither of the two?

An even or odd function can be simply checked by looking at the symmetry of the graph about the x and y-axis.

## Answer: Replacing x with -x in the function, tells the nature of the graph of the function, as per the cases discussed in the solution.

If the graph is neither symmetric about x nor y, then it is neither odd nor even function.

**Explanation:**

Let us suppose a function f (x) is given.

Now there are three different conditions to find out the nature of the graph of this function. They are as follows:

Case 1) If f (x) = f (-x), then the graph will be an even function, i.e it will be symmetric about the y axis.

Case 2) If f (x) = - f (-x), then the graph will be an odd function, i.e it will be symmetric about the x-axis.

Case 3) If f (x) is neither equal to f (-x) nor equal to -f (-x), then the graph of f (x) is neither even nor odd.