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−4∣+1
First, we will take a look at the given graph.
As we can see, each y-value of f is multiplied by 21 - this is a vertical shrink. To write the function rule g(x), let's look at a table.
Vertical Stretch or Shrink | |
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Vertical stretch, a>1y=af(x)
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Vertical shrink, 0<a<1y=af(x)
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To verify your answer, enter the function rules in the calculator by pushing Y= and writing them in the first and second rows. Next, by pushing GRAPH, the calculator will draw the graphs of the functions.
Looking at the graph, we can confirm that our solution is correct.