To analyze this problem, I’ll examine the graph provided and determine where the function is increasing, decreasing, or constant based on the intervals.

Solution:

The graph shows a function divided into three main regions based on its slope (positive, negative, or flat). Let’s break it down:

1. Increasing interval: The function rises as $x$ increases from $-2.2$ to $2.2$.

   • Answer: $(-2.2, 2.2)$

2. Decreasing interval: The function decreases as $x$ moves left from $-\infty$ to $-2.2$ and also as $x$ moves right from $2.2$ to $+\infty$.

   • Answer: $(-\infty, -2.2) \cup (2.2, \infty)$

3. Constant interval: The function remains constant only at $x = -2.2$ and $x = 2.2$. Since these are single points, no intervals apply for "constant."

   • Answer: No constant intervals.

Final Answers:

a. Increasing interval: $(-2.2, 2.2)$
b. Decreasing interval: $(-\infty, -2.2) \cup (2.2, \infty)$
c. Constant interval: None

Would you like further clarification on this?

Related Questions:

1. How do you find intervals of increase and decrease without a graph?
2. What role does the derivative play in determining these intervals?
3. Can functions have multiple increasing and decreasing intervals?
4. What are examples of real-world applications of analyzing these intervals?
5. How do endpoints influence the classification of intervals?

Tip:

Always check if the graph has flat regions or constant segments—they might not occur on every graph but are worth identifying!