To determine the appropriate transformation for the curves in the described graphs, we need to analyze the general behavior of the curves based on their plotted points and the factors involved.
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Vertical Compression vs. Vertical Stretch:
- A vertical compression occurs when a graph is squeezed toward the x-axis (the factor, k, is between 0 and 1).
- A vertical stretch occurs when a graph is pulled away from the x-axis (the factor, k, is greater than 1).
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Characteristics of the Curves:
- If both graphs pass through the specified points and show a behavior where their values are reduced (compared to their parent functions), they represent vertical compressions.
- If the values of the curves exceed those of their respective parent functions at the same x-values, they represent vertical stretches.
Since both graphs are described as representing transformations, assuming they pass through the points as defined, here are the possibilities:
Given that the responses suggest differences in the factors of k being different or the same, one can assess either stretches or compressions but must stick to the data provided, which doesn't specify exact functional forms or intervals.
However, if your assessment is primarily based on the nature of the plotted points (without visual aids):
- If the curves pass beneath the parent function, likely, that indicates a compression (not enough rise).
- If the curves rise more than the parent function, that would denote a stretch.
Thus, assuming a common vertical transformation is implied without conflicting roles and since both mention vertical behavior changing in some form, the most general response could be:
Both graphs represent vertical stretches, although they use different factors of k.
This covers the idea that both manipulations elevate their values over the originals while allowing variance in the strict measure of k, without precise visual data.
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