What transformations change the graph of $$ f(x) $$ to the graph of $$ g(x) $$ ? $$ f(x)=x^{2} $$ to $$ g(x)=(x+5)^{2}-9 $$ a The graph of $$ g(x) $$ is the graph of $$ f(x) $$ translated to the left 9 units and down 5 units. o The graph of $$ g(x) $$ is the graph of $$ f(x) $$ translated to the right 9 units and up 5 units. o The graph of $$ g(x) $$ is the graph of $$ f(x) $$ translated to the right 5 units and up 9 units. The graph of $$ g(x) $$ is the graph of $$ f(x) $$ translated to the left 5 units and down 9 units.

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The graph of $$ g(x) $$ is translated left 5 units and down 9 units. To determine the transformations that change the graph of $$ f(x) = x^2 $$ to the graph of $$ g(x) = (x + 5)^2 - 9 $$, we can analyze the changes step by step. 1. **Starting Function**: $$ f(x) = x^2 $$ 2. **Horizontal Shift**: The term $$ (x + 5) $$ indicates a horizontal shift. The graph of $$ f(x) $$ is shifted to the left by 5 units. This is because adding a positive number inside the function (to $$ x $$) results in a leftward shift. 3. **Vertical Shift**: The term $$ -9 $$ indicates a vertical shift. The graph is shifted down by 9 units because we are subtracting 9 from the entire function. Putting these transformations together, we can summarize: - The graph of $$ g(x) $$ is the graph of $$ f(x) $$ translated **left 5 units** and **down 9 units**. Thus, the correct answer is: **The graph of $$ g(x) $$ is the graph of $$ f(x) $$ translated to the left 5 units and down 9 units.**

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