# How to determine if a graph is even or odd?

We will use the concept of functions to find if the graph is even or odd.

## Answer: If we substitute x with -x (negative x) in the function f(x) and the value of function f(x) becomes negative i.e. f(-x) = -f(x) for all x, then the function is known as odd function. If the value of function does not change i.e. f(-x) = f(x) for all x, then the function is known as an even function.

Let us see the solution in detail.

**Explanation:**

Let us consider a function f(x).

Odd function: If we substitute x with -x in the function f(x) and the value of function becomes negative, then the function is known as odd function.

Hence, for odd function f(-x) = - f(x), for all x.

For example let us consider a function f(x) = x^{3 }.

If we substitute x by - x in above function then we find out that f(-x) = - x^{3 }.

Hence , f(x) = x^{3} is an odd function.

Even function: If we substitute x with -x in the function f(x) and the value of function does not change, then the function is known as an even function.

Hence, for even function f(x ) = f(-x), for all x.

For example let us consider a function f(x) = x^{2}

If we substitute x by -x in above function then we find out that f (-x) = x^{2}.

Hence, f(x) = x^{2} is an even function.

### Thus, if we substitute x with -x (negative x) in the function f(x) and the value of function f(x) becomes negative i.e. f(-x) = -f(x) for all x, then the function is known as odd function. If the value of function does not change i.e. f(-x) = f(x) for all x, then the function is known as an even function.

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