Answer :
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Answer:
Let's analyze the problem:
Understanding the given information:
We hadve a graph of an absolute value function f(x) with a vertex at (0, 2).
We have a table of values for another absolute value function g(x).
The relationship between f(x) and g(x) is given by g(x) = f(x + k).
Goal:
Find the value of k.
Analysis:
The key to solving this problem lies in understanding the transformation represented by g(x) = f(x + k). This transformation is a horizontal shift of the graph of f(x).
If k is positive, the graph of f(x) is shifted k units to the left.
If k is negative, the graph of f(x) is shifted k units to the right.
Since we don't have the exact values of g(x) for specific x values, we can't pinpoint the exact shift. However, we can make an educated guess based on the general shape of absolute value functions.
Possible solution:
Given that the vertex of f(x) is at (0, 2) and the table for g(x) starts with x = -1, it's likely that g(x) is a shifted version of f(x) to the right. This would indicate a negative value for k.
Based on this analysis, the most likely answer is k = -2.
However, without the exact values of g(x) for different x values, we cannot be completely certain.
To get a definitive answer, i would need more information about the function g(x), such as specific points on the graph or additional values in the table.
