This applet shows you the effect of each transformation on a graph.

Sketch the following curves on paper and check your graphs using the above applet:

y = 2 sin(x), | y = 0.5 sin(x), | y = sin(2x), | y = sin(0.5x), | y = sin(x - 1), | y = sin(x + 1) |

y = sin(x) + 1, | y = sin(x) - 1, | y = (x+1)^{2}, | y = (x-1)^{2}, | y = x^{2} + 1, | y = x^{2} - 1 |

y = 1/x, | y = 1/(x-1), | y = exp(x-1), | y = exp(x) - 1 |

y = a f(x) | The graph is scaled by factor a parallel to the y-axis. |

If a is negative, the graph is reflected in the x-axis. | |

y = f(ax) | The graph is scaled by factor 1/a parallel to the x-axis. |

If a is negative, the graph is reflected in the y-axis. | |

y = f(x + a) | The graph is translated in the direction of the negative x-axis by a units. |

If a is negative, the graph is translated in the direction of the positive x-axis. | |

y = f(x) + a | The graph is translated in the direction of the positive y-axis by a units. |

If a is negative, the graph is translated in the direction of the negative y-axis. |

Right-click here to download this page and the Java Class File.

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