# example of increasing/decreasing/monotone function

The function^{} $f(x)={e}^{x}$ is strictly increasing^{} and hence strictly monotone. Similarly $g(x)={e}^{-x}$ is strictly decreasing and hence strictly monotone. Consider the function $h:[1,10]\mapsto [1,5]$ where $h(x)=\sqrt{x-4\sqrt{x-1}+3}+\sqrt{x-6\sqrt{x-1}+8}$. It is not strictly monotone since it is constant on an interval, however it is decreasing and hence monotone^{}.

Title | example of increasing/decreasing/monotone function |
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Canonical name | ExampleOfIncreasingdecreasingmonotoneFunction |

Date of creation | 2013-03-22 13:36:08 |

Last modified on | 2013-03-22 13:36:08 |

Owner | Johan (1032) |

Last modified by | Johan (1032) |

Numerical id | 4 |

Author | Johan (1032) |

Entry type | Example |

Classification | msc 26A06 |