Given function , then:
1. Any transformation which acts on the whole function, produces an up/down type of change in which the change goes in the direction expected (eg ‘+’ moves up etc.).
2. Any transformation which acts on the variable within the function, produces a left/right type of change in which the change goes in the opposite direction to that expected (eg ‘+’ moves left)
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Acting on the function (up/down change) Ie ‘as expected’ |
Acting on the variable (left/right change) Ie ‘opposite to expected’ |
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Transformation |
Movement |
Transformation |
Movement |
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‘n’ places up |
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‘n’ places to left |
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‘n’ places down |
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‘n’ places to right |
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Stretches by factor of ‘n’ up and down |
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Squashes by factor of ‘n’ left/right |
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Squashes by factor of ‘n’ up down |
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Stretches by factor ‘n’ left/right |
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Reflects in x-axis |
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Reflects in y-axis |
Remember that there may be more than one transformation acting on any one function.
e.g. is simply with the +4 moving the whole curve up 4 places and the -2 moving the whole curve 2 places to the right.