To analyze the graph and answer the questions, let's go through each part step-by-step:

Observing the Graph

The graph shows a curve, which appears to be increasing from left to right. This suggests that the function is increasing over certain intervals.

Part (a): Identify Intervals where the Function is Increasing

To determine where the function is increasing, look for sections where the graph moves upward as $x$ increases. The curve starts from around $x = -4$ and consistently rises as it moves to the right. Therefore, we can say:

• The function is increasing on the interval $(-4, \infty)$.

Part (b): Identify Intervals where the Function is Decreasing

The function is decreasing on intervals where the graph moves downward as $x$ increases. Since the entire graph moves upward as $x$ increases, there are no intervals where the function is decreasing.

So, the answer for part (b) is:

• There are no intervals where the function is decreasing.

Part (c): Identify Intervals where the Function is Constant

The function is constant where the graph is a horizontal line. There is no such section on this graph; it is always either moving up (increasing) or sloping.

So, the answer for part (c) is:

• There are no intervals where the function is constant.

Final Answers:

1. (a) The function is increasing on the interval $(-4, \infty)$.
2. (b) There are no intervals where the function is decreasing.
3. (c) There are no intervals where the function is constant.

Let me know if you'd like any more details, or if you have further questions on this!

Here are five related questions that build on this topic:

1. What does it mean for a function to be increasing or decreasing in a real-world context?
2. How can you determine the intervals of increase and decrease from a function's derivative?
3. What is the significance of a constant interval in a function, and where do we usually see such behavior?
4. How does one determine whether a function is increasing or decreasing without a graph?
5. What types of functions are always increasing or always decreasing?

Tip: When identifying intervals of increase or decrease, look at how the $y$-values change as $x$-values increase.