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)

Question

Answer 1

To determine the transformation of the graph of

compared to the graph of

, we need to analyze the given function

.The function

is obtained by shifting the graph of

horizontally and vertically. Let's analyze the horizontal shift first:The term

inside the function

indicates a horizontal shift. Specifically, it represents a shift of 1 unit to the left. This is because the input value

is being increased by 1 before being passed into the function

.Next, let's analyze the vertical shift:The term

outside the function

indicates a vertical shift. Specifically, it represents a shift of 6 units upwards. This is because the output value of the function

is being increased by 6 before being passed into the function

.Therefore, the correct answer is:D. The graph of

is shifted 1 unit to the left and 6 units above the graph of

.

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