The problem you're working on requires determining the intervals where the function is increasing. From the image, the function appears to be represented by a graph with a piecewise linear plot.

Steps to Determine the Intervals of Increase:

1. Observe the Slope of the Function: The function is increasing wherever the graph has a positive slope (i.e., the line segment moves upwards as you move from left to right).

2. Identify the Intervals: Look at the sections of the graph where the function goes upwards. These are the intervals where the function is increasing.

3. Write the Intervals: Express the intervals using the appropriate notation, generally using parentheses to indicate open intervals where the endpoints are not included unless specified otherwise.

Analysis:

From the graph in the image:

• The function appears to increase from around $x = -3$ to $x = -1$.
• This interval can be expressed as $(-3, -1)$.

Thus, the interval where the function is increasing is approximately $(-3, -1)$.

Follow-up Questions:

1. What is the interval where the function is decreasing?
2. How can we determine if the function is constant on any interval?
3. Can you identify the coordinates of the turning points on the graph?
4. How does the graph help in determining whether a function is increasing or decreasing?
5. What would the derivative of this function look like if it were continuous?

Tip:

When analyzing functions graphically, always pay close attention to the slopes of the line segments to determine where the function is increasing, decreasing, or constant.