To determine where the function is increasing, decreasing, and constant from the given graph, let’s analyze its behavior based on the plotted curve:

1. Intervals where the function is increasing:

• The function increases when moving to the right along the curve and the graph rises.
• This occurs in the interval from $x = -6$ to $x = -4$, and from $x = 0$ to $x = 2$.

2. Intervals where the function is decreasing:

• The function decreases when moving to the right and the graph falls.
• This occurs in the interval from $x = -4$ to $x = -2$.

3. Intervals where the function is constant:

• The function is constant where the graph is a horizontal line (no change in $y$-values).
• This occurs in the interval from $x = 2$ to $x = 6$.

Final Results:

• Increasing intervals: $(-6, -4) \cup (0, 2)$
• Decreasing intervals: $(-4, -2)$
• Constant intervals: $(2, 6)$

Would you like further details or clarification?

Here are 5 questions related to this topic:

1. How can we determine whether a function is increasing or decreasing from its derivative?
2. What does a constant function imply about the slope of the function in that interval?
3. How can we identify turning points in a graph?
4. Can a function have multiple intervals of constant values?
5. What is the significance of critical points in determining increasing or decreasing behavior?

Tip: The first derivative of a function gives critical information about where the function is increasing or decreasing. A positive derivative means increasing, and a negative derivative means decreasing.