2. Transformations of Linear and Absolute Value Functions
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Determine which operation should be used for each transformation and apply the desired transformations in order.
g(x)=∣x−1∣−3
First, we will take a look at the given graph.
As we can see, each y-value of f is shifted 1 unit to the right and 3 units down. To write the function rule g(x) let's look at a table of transformations.
Transformations of f(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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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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