The function g(x)=f(x+1)+6 Which of the following is true about the graph of g(x) A The graph of g(x) is shifted 1 units to the right and 6 units below the graph of f(x) B The graph of g(x) is shifted 1 units to the left and 6 units below the graph of f(x) C The graph of g(x) is shifted 1 units to the right and 6 units above the graph of f(x) D The graph of g(x) is shifted 1 units to the left and 6 units above the graph of f(x)

To determine the transformation of the graph of $g(x)$ compared to the graph of $f(x)$, we need to analyze the given function $g(x) = f(x+1) + 6$.<br /><br />The function $g(x)$ is obtained by shifting the graph of $f(x)$ horizontally and vertically. Let's analyze the horizontal shift first:<br /><br />The term $(x+1)$ inside the function $f(x+1)$ indicates a horizontal shift. Specifically, it represents a shift of 1 unit to the left. This is because the input value $x$ is being increased by 1 before being passed into the function $f(x)$.<br /><br />Next, let's analyze the vertical shift:<br /><br />The term $+6$ outside the function $f(x+1)$ indicates a vertical shift. Specifically, it represents a shift of 6 units upwards. This is because the output value of the function $f(x+1)$ is being increased by 6 before being passed into the function $g(x)$.<br /><br />Therefore, the correct answer is:<br /><br />D. The graph of $g(x)$ is shifted 1 unit to the left and 6 units above the graph of $f(x)$.