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.
B.
C.
D.
Graph shape: a horizontal blue line segment with solid endpoints, originally at $y = 2$ from $x = -2$ to $x = 2$; after shifting down 2 units, $g(x)$ should be a horizontal blue line segment at $y = 0$ from $x = -2$ to $x = 2$. position_hint: top-left
Graph shape: option A shows a horizontal blue line segment near $y = 4$, from $x = -2$ to $x = 2$. position_hint: top-right
Graph shape: option B shows a horizontal blue line segment near $y = 3$, from $x = -2$ to $x = 2$. position_hint: top-right
Graph shape: option C shows a horizontal blue line segment near $y = 1$, from $x = -2$ to $x = 2$. position_hint: bottom-left
Graph shape: option D shows a horizontal blue line segment on the x-axis, from $x = -2$ to $x = 2$. position_hint: bottom-right
1. **State the problem:** We are given the graph of $y = f(x)$, which is a horizontal line segment at $y = 2$ from $x = -2$ to $x = 2$. We want to graph $g(x) = f(x) - 2$.
2. **Understand the transformation:** The function $g(x) = f(x) - 2$ means we take the original function $f(x)$ and shift it down by 2 units.
3. **Apply the transformation:** Since $f(x) = 2$ on the interval $[-2, 2]$, then
$$g(x) = 2 - 2 = 0$$
for all $x$ in $[-2, 2]$.
4. **Interpret the result:** The graph of $g(x)$ is a horizontal line segment at $y = 0$ from $x = -2$ to $x = 2$.
5. **Choose the correct graph:** Among the options, the graph that shows a horizontal line segment on the x-axis (i.e., $y=0$) from $x = -2$ to $x = 2$ is option D.
**Final answer:** The correct graph of $g(x) = f(x) - 2$ is option D.