Question: Use the graph of $y = f(x)$ to graph the function $g(x) = f(x) - 2$. $y = f(x)$ Choose the correct graph of $g$ below. A. position_hint \in \{top-right\}: horizontal blue line segment from $x = -2$ to $x = 2$ at $y = 4$. B. position_hint \in \{top-right\}: horizontal blue line segment from $x = -2$ to $x = 2$ at $y = 3$. C. position_hint \in \{bottom-right\}: horizontal blue line segment from $x = -2$ to $x = 2$ at $y = 1$. D. position_hint \in \{bottom-right\}: horizontal blue line segment from $x = -2$ to $x = 2$ at $y = 0$.

1. **State the problem:** We are given a function $y = f(x)$ and asked to graph $g(x) = f(x) - 2$ using the graph of $f(x)$. 2. **Understand the transformation:** The function $g(x) = f(x) - 2$ represents a vertical shift of the graph of $f(x)$ downward by 2 units. 3. **Apply the transformation:** If the original graph $f(x)$ has a horizontal line segment from $x = -2$ to $x = 2$ at some height $y = h$, then the graph of $g(x)$ will have the same segment shifted down by 2 units, i.e., at $y = h - 2$. 4. **Identify the original height:** From the options, the original $f(x)$ segment is at $y = 3$ or $y = 4$ or $y = 1$ or $y = 0$. Since $g(x) = f(x) - 2$, the correct graph of $g$ should be the original graph shifted down by 2. 5. **Check each option:** - If $f(x)$ is at $y = 4$, then $g(x)$ is at $4 - 2 = 2$ (not listed). - If $f(x)$ is at $y = 3$, then $g(x)$ is at $3 - 2 = 1$ (option C). - If $f(x)$ is at $y = 1$, then $g(x)$ is at $1 - 2 = -1$ (not listed). - If $f(x)$ is at $y = 0$, then $g(x)$ is at $0 - 2 = -2$ (not listed). 6. **Conclusion:** The correct graph of $g$ is option C: a horizontal blue line segment from $x = -2$ to $x = 2$ at $y = 1$. **Final answer:** Option C.