# Transformations of Graphs

Shrink, Stretch, Shifts

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Graphs | Equations of Graphs | Term |
---|---|---|

f(x) = x^2; g(x) = (x - 2)^2 | Horizontal Shift Right | |

f(x) = x^2; g(x) = (x + 2)^2 | Horizontal Shift Left | |

f(x) = x^2; g(x) = x^2 + 2 | Vertical Shift Up | |

f(x) = x^2; g(x) = x^2 - 2 | Vertical Shift Down | |

f(x) = x^2; y = (1/2)* f(x^2) | Vertical Shrink | |

f(x) = x^2; y = 2* f(x^2) | Vertical Stretch | |

f(x) = sqrt(x); g(x) = - sqrt(x) | Reflection about the x-axis | |

f(x) = sqrt(x); g(x) = sqrt(- x) | Reflection about the y-axis | |

f(x) = sin x; g(x) = sin ((1/2)x) | Horizontal Stretch | |

f(x) = sin x; g(x) = sin(2x) | Horizontal Shrink | |

f(x) = x^2; g(x) = (2x^2) | Horizontal Shrink | |

f(x) = x^2; g(x) = (1/2)x^2 | Horizontal Stretch | |

y = cf(x); 0 < c < 1 | Vertical Shrink | |

y = f(cx); c > 1 | Horizontal Shrink | |

y = cf(x); c > 1 | Vertical Stretch | |

y = f(cx); 0 < c < 1 | Horizontal Stretch | |

y = f(x); y = f(x-c) | Horizontal Shift Right | |

y = f(x); y = f(x-(-c)) | Horizontal Shift Left | |

y = f(x); y = f(x) + c | Vertical Shift Up | |

y = f(x); y = f(x) - c | Vertical Shift Down | |

y = f(x); y = f(-x) | Reflection on the Y Axis | |

y = f(x); y = -f(x) | Reflection on the X Axis |