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A translation of a function is a transformation that moves a function graph in some direction, without any rotation, shrinking, or stretching. A function's graph is vertically translated by adding a number to — or subtracting from — the function rule.
$g(x)=f(x)±k$
$g(x)=f(x±h)$
Translations of $f(x)$ | |
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Vertical Translations | Translation up $k$ units, $k>0$ $y=f(x)+k$ |
Translation down $k$ units, $k>0$ $y=f(x)−k$ | |
Horizontal Translations | Translation to the right $h$ units, $h>0$ $y=f(x−h)$ |
Translation to the left $h$ units, $h>0$ $y=f(x+h)$ |
Transformations of $f(x)$ | |
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Reflections | In the $x-$axis $y=-f(x)$ |
In the $y-$axis $y=f(-x)$ |
Transformations of $f(x)$ | |
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Vertical Stretch or Shrink | Vertical stretch, $a>1$ $y=af(x)$ |
Vertical shrink, $0<a<1$ $y=af(x)$ |
Transformations of $f(x)$ | |
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Horizontal Stretch or Shrink | Horizontal stretch, $0<b<1$ $y=f(bx)$ |
Horizontal shrink, $b>1$ $y=f(bx)$ |