Questions: Use the graph of (y=f(x)) to graph the function (g(x)=f(x+3)+2). Choose the correct graph of (g) below. A. B. C. D.

Transcript text: Use the graph of $y=f(x)$ to graph the function $g(x)=f(x+3)+2$. Choose the correct graph of $g$ below. A. B. $\qquad$ C. D.

Solution

Step 1: Identify the Transformation

The function $ g(x) = f(x + 3) + 2 $ involves two transformations of the function $ f(x) $:

Step 2: Apply the Horizontal Shift

Shift the graph of $ f(x) $ to the left by 3 units. This means every point on the graph of $ f(x) $ will move 3 units to the left.

Step 3: Apply the Vertical Shift

After shifting the graph to the left, shift it upwards by 2 units. This means every point on the graph will move 2 units up.

The correct graph of $ g(x) $ is option C.

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