1. The problem asks how the graph of $g(x) = 2 - \sqrt{x}$ is related to the graph of $f(x) = \sqrt{x}$. We need to analyze the transformation from $f(x)$ to $g(x)$. 2. Recall the basic transformations: - Adding a constant outside the function shifts the graph vertically. - Multiplying the function by $-1$ reflects it across the x-axis. 3. Write $g(x)$ as: $$g(x) = 2 - \sqrt{x} = 2 + (-1) \cdot \sqrt{x}$$ This means $g(x)$ is $f(x)$ reflected in the x-axis (due to the $-1$ multiplier) and then shifted up by 2 units (due to the $+2$). 4. Therefore, the graph of $g(x)$ is the graph of $f(x)$ reflected in the x-axis and shifted up 2 units. 5. This matches option B. 6. Sketching the graph: The original $f(x) = \sqrt{x}$ starts at $(0,0)$ and increases to the right. The graph of $g(x)$ starts at $(0,2)$ and decreases to the right because of the reflection. Final answer: B. The graph of $g(x)$ is the graph of $f(x)$ reflected in the x-axis and shifted up 2 units.