Describe how the graph of the function \( g(x)=f(x+2)-6 \) a transformation of the original function \( f \). The graph of \( g(x)=f(x+2)-6 \) is a horizontal shift to the right 6 units and a vertical shift down 2 units of the graph of \( f \). The graph of \( g(x)=f(x+2)-6 \) is a horizontal shift to the left 2 units and a vertical shift down 6 units of the graph of \( f \). The graph of \( g(x)=f(x+2)-6 \) is a horizontal shift to the right 2 units and a vertical shift down 6 units of the graph of \( f \). The graph of \( g(x)=f(x+2)-6 \) is a horizontal shift to the left 6 units and a vertical shift up 2 units of the graph of \( f \).

The correct description of the transformation for the function \( g(x) = f(x+2) - 6 \) is: **The graph of \( g(x) = f(x+2) - 6 \) is a horizontal shift to the left 2 units and a vertical shift down 6 units of the graph of \( f \).** ### Explanation: 1. **Horizontal Shift:** - The expression inside the function \( f(x+2) \) affects the horizontal position of the graph. - The \( +2 \) inside the function indicates a **shift to the left** by 2 units. (Remember, adding inside the function moves the graph in the opposite direction.) 2. **Vertical Shift:** - The \( -6 \) outside the function affects the vertical position of the graph. - This indicates a **shift downward** by 6 units. ### Summary of Transformations: - **Left Shift:** 2 units - **Downward Shift:** 6 units **Therefore, option 2 accurately describes the transformation:** > **The graph of \( g(x) = f(x+2) - 6 \) is a horizontal shift to the left 2 units and a vertical shift down 6 units of the graph of \( f \).**