1. Graphing Square Root Functions
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Consider vertical and horizontal translations, stretches and shrinks, and reflections.
Transformation: A horizontal translation left 4 units followed by a vertical shrink by a factor of 21 and a vertical translation up 1 unit.
Graph:
We want to describe the transformations of the parent function f(x)=x represented by g(x)=21x+4+1.
Let's look at the possible transformations. Then we can more clearly identify the ones being applied.
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 Shrink | Vertical stretch, a>1y=af(x)
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Vertical shrink, 0<a<1y=af(x)
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Horizontal Translations | Translation right h units, h>0y=f(x−h)
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Translation left h units, h>0y=f(x+h)
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