On Reduction, 3 of 11

Graphs of Reduction and Protraction

     Here's a graph of     y  =  x <+> 1 :

                                  .*     |

                                  .*     |

                                 . *     |

                              .    *     |

               _. _  _ ._  _  _  _ *_  _ |_1_  _  _  _  _  _  _  _

                                   *     |        .      .

                                   *     | .

                                   *     .                        

                                 -1*   . |

                                   *  .  |

                                   * .   |

     In general the graph of  y=x<+>a  will have a vertical asymptote at x=(-a), a horizontal asymptote at y=a, and it will go through (0,0).

     Here’s a graph of       y  =  1 <-> x :

                                   |     *  .

                                   |     *   .

                                   |     *     .

                                   |     *        .     

               _  _  _  _  _  _  _1|_  _ * _  _  _  _ ._  _  _  _ 

                .      .           |     *               

                              .    |     * 

                                   .     *                      

                                   | .   *1

                                   |   . *

                                   |    .*

                                   |    .*

     In general the graph of  y=a<->x will have a vertical asymptote at x=a, a horizontal asymptote at y=a, and it will go through (0,0).