Looking at the graph provided in the question, let's go over the problem step by step.

Observations from the Graph:

• The graph represents a function $f(x)$ over the interval $[-4, 4]$.
• The function seems to have different behaviors in different intervals.

Breakdown of Each Part:

(a) Open intervals on which the function is increasing:

• The function is increasing where its slope is positive.
• From the graph, we see that the function increases from $x = 0$ to $x = 4$.

Answer: $(0, 4)$

(b) Open intervals on which the function is decreasing:

• The function decreases where its slope is negative.
• From the graph, the function decreases from $x = -4$ to $x = 0$.

Answer: $(-4, 0)$

(c) Open intervals on which the function is constant:

• The function is constant where its slope is zero (a horizontal line).
• There are no horizontal lines in this graph, so the function is never constant.

Answer: The function is never constant.

Conclusion:

1. (a) The function is increasing on the interval $(0, 4)$.
2. (b) The function is decreasing on the interval $(-4, 0)$.
3. (c) The function is never constant.

Would you like any more details or clarification on these answers?

Here are five questions related to this:

1. How do you determine the slope of a function visually from a graph?
2. What does the interval notation represent in terms of function behavior?
3. How would the function behave if there were a horizontal section on the graph?
4. How do critical points relate to increasing and decreasing intervals?
5. What is the difference between a closed and open interval in graph interpretation?

Tip: When using interval notation, always remember to use round brackets for open intervals (where the endpoints are not included).