Question: Use the graph to determine
(a) open intervals on which the function is increasing, if any.
(b) open intervals on which the function is decreasing, if any.
(c) open intervals on which the function is constant, if any.
(a) Select the correct choice below, and if necessary, fill in the answer box to complete your choice.
A. The function is increasing on the interval(s) (Type your answer in interval notation. Use a comma to separate answers as needed.)
B. The function is never increasing.
(b) Select the correct choice below, and if necessary, fill in the answer box to complete your choice.
A. The function is decreasing on the interval(s) (Type your answer in interval notation. Use a comma to separate answers as needed.)
B. The function is never decreasing.
(c) Select the correct choice below, and if necessary, fill in the answer box to complete your choice.
A. The function is constant on the interval(s) (Type your answer in interval notation. Use a comma to separate answers as needed.)
B. The function is never constant.
Graph: a single continuous curve in the center-right of the page, with a local maximum near $x = -2$ and $y = -1$, a local minimum near $x = -1$ and $y = -2$, then another local maximum near $x = 0$ and $y = -1$, with arrows showing the graph continues downward near $x \approx -3$ and $x \approx 1$; position_hint \in \{center, top-right\}.
1. **State the problem:** We need to determine the open intervals where the function is increasing, decreasing, or constant based on the given graph.
2. **Recall definitions:**
- A function is **increasing** on an interval if as $x$ increases, $f(x)$ also increases.
- A function is **decreasing** on an interval if as $x$ increases, $f(x)$ decreases.
- A function is **constant** on an interval if $f(x)$ remains the same as $x$ changes.
3. **Analyze the graph:**
- The graph has a local maximum near $x = -2$, $y = -1$.
- Then it decreases to a local minimum near $x = -1$, $y = -2$.
- Then it increases again to a local maximum near $x = 0$, $y = -1$.
- The graph continues downward beyond $x \approx 1$ and $x \approx -3$.
4. **Determine intervals:**
- From the left (near $x \approx -3$) to $x = -2$, the graph is increasing (going up to the local max).
- From $x = -2$ to $x = -1$, the graph is decreasing (going down to the local min).
- From $x = -1$ to $x = 0$, the graph is increasing again (going up to the local max).
- From $x = 0$ to $x \approx 1$, the graph is decreasing.
- There are no flat (constant) intervals visible.
5. **Write intervals in interval notation:**
- Increasing on $(-3, -2)$ and $(-1, 0)$.
- Decreasing on $(-2, -1)$ and $(0, 1)$.
- Constant on no intervals.
6. **Final answers:**
- (a) Increasing intervals: $(-3, -2), (-1, 0)$
- (b) Decreasing intervals: $(-2, -1), (0, 1)$
- (c) Constant intervals: none