Suppose that g(x) = f(x) – 2. Which statement best compares the graph of g(x) with the graph of f(x)?A.The graph of g(x) is vertically stretched by a factor of 2.B.The graph of g(x) is shifted 2 units up.C.The graph of g(x) is shifted 2 units down.D.The graph of g(x) is shifted 2 units to the left
Question
Suppose that g(x) = f(x) – 2. Which statement best compares the graph of g(x) with the graph of f(x)?A.The graph of g(x) is vertically stretched by a factor of 2.B.The graph of g(x) is shifted 2 units up.C.The graph of g(x) is shifted 2 units down.D.The graph of g(x) is shifted 2 units to the left
Solution
To answer the question, let's analyze the given function transformation step by step.
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Given Functions: We have .
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Understanding the Transformation: The function is derived from by subtracting 2 from . This means that for every value of , the value of is 2 units less than the value of .
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Graphical Interpretation: Subtracting a constant from a function results in a vertical shift of the graph of . Specifically, subtracting 2 shifts the graph downward by 2 units.
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Conclusion: The graph of is shifted 2 units down compared to the graph of .
Therefore, the correct statement is: C. The graph of g(x) is shifted 2 units down.
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