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

Prerequisite for this articles is listed below.

The function is even function, if for every x in domain of .

$f(\u2013x)=f\left(x\right)$

for example,

Let be a function where

$f\left(x\right)={x}^{2}$

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 function is odd function if for every in the domain of .

$f(\u2013x)=\u2013f\left(x\right)$

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.

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