6. Families of Functions
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Consider vertical and horizontal translations, stretches and compressions, and reflections. To draw the graph, choose a point on the parent function and apply the transformations to the point.
Description of Transformation: Vertical stretch by a factor of 2 and vertical translation up by 1 unit.
Graph:
To describe and graph the given transformation, h(x)=2f(x)+1, let's look at all of the possible transformations. Then we can more clearly identify the transformations being applied to the parent function f(x)=-2x.
Transformations of f(x) | |
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Vertical Translations | Translation up k units, k>0y=f(x)+k
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Translation down k units, k>0y=f(x)−k
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Vertical Stretch or Compression | Vertical stretch, a>0y=af(x)
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Vertical compression, 0<a<1y=af(x)
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