The graph of equation has symmetry along the x-axis or y-axis. In this article, the symmetry of a graph of function is defined in terms of even and odd function.

Prerequisite for this articles is listed below.

## Even Function

Let’s understand the even functions first. The function is even function, if for every x in domain of .

f(-x) = f(x)

For example,

Let be a function where

f(x) = x^2

The function will square any input value for and output . Let us put some values for , see the following table of values.

x | y = f(x) | point |

-2 | 4 | (-2, 4) |

-1 | 1 | (-1, 1) |

0 | 0 | (0, 0) |

1 | 1 | (1, 1) |

2 | 4 | (2, 4) |

The table shows that any values is equal to .

The graph of even function is symmetric along the y-axis.

**Odd Functions**

The odd function is different from even function in terms of symmetry of graph of the function. The function is odd function if for every in the domain of .

f(-x) = -f(x)

Consider the following table of points for the function .

x | y = f(x) = x + 1 | point |

-3 | -2 | (-3, -2) |

-2 | -1 | (-2, -1) |

-1 | 0 | (-1, 0) |

0 | 1 | (0, 1) |

1 | 2 | (1, 2) |

2 | 3 | (2, 3) |

The graph of odd function shows that is .

The graph of odd function is symmetric along the y-axis.