Problemas

2 The function g(x)=f(x+2) Which of the following Is true about the graph of g(x) A The graph of g(x) is shifted 2 units to the right of the graph of f(x) B The graph of g(x) is shifted 2 units to the left of the graph of f(x) C The graph of g(x) is shifted 2 units below the graph of f(x) The graph of g(x) is shifted 2 units above the graph of f(x)
Solución
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B
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The function $g(x)=f(x+2)$ is a transformation of the function $f(x)$. In this case, the "+2" inside the function $f(x+2)$ indicates a horizontal shift of the graph. Specifically, it means that the graph of $g(x)$ is shifted 2 units to the left of the graph of $f(x)$. This is because the "+2" is inside the function, affecting the x-values, which correspond to the horizontal direction. If it were outside the function, such as in $f(x)=g(x+2)$, it would indicate a vertical shift. Therefore, the correct answer is B: The graph of $g(x)$ is shifted 2 units to the left of the graph of $f(x)$.
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