To solve this problem, we need to analyze the provided graph and identify the intervals where the function is increasing, decreasing, or constant.

Analyzing the Graph

From the graph:

• The function has a segment that goes upwards from left to right.
• The function also has a segment that goes downwards from left to right.
• There is a flat segment where the function does not increase or decrease.

Step-by-Step Analysis:

1. Increasing Intervals:

   • The function is increasing where the graph goes upward. This happens from $x = -2$ to $x = 1$.

2. Decreasing Intervals:

   • The function is decreasing where the graph goes downward. This occurs from $x = 1$ to $x = 4$.

3. Constant Intervals:

   • The function is constant where the graph is a horizontal line. This occurs from $x = 4$ to $x = 5$.

Answers in Interval Notation:

a. Increasing Interval(s):

• The function is increasing on the interval: $(-2, 1)$.

b. Decreasing Interval(s):

• The function is decreasing on the interval: $(1, 4)$.

c. Constant Interval(s):

• The function is constant on the interval: $(4, 5)$.

Correct Choices:

• a. Choice A: The function is increasing on the interval(s) $(-2, 1)$.
• b. Choice A: The function is decreasing on the interval(s) $(1, 4)$.
• c. Choice A: The function is constant on the interval(s) $(4, 5)$.

Would you like more details on this problem or have any questions?

Further Related Questions:

1. How do you determine intervals where a function is increasing, decreasing, or constant?
2. What is the difference between an open and a closed interval in interval notation?
3. How would the answers change if the graph was modified to have different slopes or constant segments?
4. What role do endpoints play in determining whether an interval is open or closed?
5. How can you find the slope of a line segment from a graph?

Tip: When using interval notation, remember that round brackets $( )$ indicate that the endpoints are not included, while square brackets $[ ]$ indicate that they are included.