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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

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Solution

To answer the question, let's analyze the given function transformation step by step.

  1. Given Functions: We have g(x)=f(x)2 g(x) = f(x) - 2 .

  2. Understanding the Transformation: The function g(x) g(x) is derived from f(x) f(x) by subtracting 2 from f(x) f(x) . This means that for every value of x x , the value of g(x) g(x) is 2 units less than the value of f(x) f(x) .

  3. Graphical Interpretation: Subtracting a constant from a function f(x) f(x) results in a vertical shift of the graph of f(x) f(x) . Specifically, subtracting 2 shifts the graph downward by 2 units.

  4. Conclusion: The graph of g(x) g(x) is shifted 2 units down compared to the graph of f(x) f(x) .

Therefore, the correct statement is: C. The graph of g(x) is shifted 2 units down.

This problem has been solved

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