Question: Determine the interval over which the graph is decreasing.
Graph: a piecewise linear graph with a horizontal ray at $y = 2$ extending left from $(1, 2)$, then a line segment decreasing from $(1, 2)$ to $(4, -1)$, then a line segment increasing from $(4, -1)$ to the upper right; position_hint = center.
$(1, 4)$
$(2, -1)$
$(\infty, -1)$
$(\infty, 4)$
1. **State the problem:** We need to find the interval where the graph is decreasing.
2. **Analyze the graph description:**
- The graph has a horizontal ray at $y=2$ extending left from $(1,2)$, so it is constant (not decreasing) on $(-\infty, 1)$.
- From $(1,2)$ to $(4,-1)$, the graph is a line segment that decreases because the $y$-value goes from $2$ down to $-1$.
- From $(4,-1)$ onwards, the graph increases.
3. **Identify the decreasing interval:**
- The graph decreases on the interval from $x=1$ to $x=4$.
4. **Express the interval:**
- The interval where the graph is decreasing is $$ (1, 4) $$.
5. **Final answer:** The graph is decreasing on the interval $(1, 4)$.