The image you've provided shows a graph of a function. It looks like you're working on finding intervals where the graph is increasing or decreasing, along with determining the relative maximum and minimum values, domain, and range.

Based on the graph and the questions provided, here's how to approach each of these:

1. Intervals where the graph is increasing:

   • The graph is increasing between the x-values where the slope is positive. From the graph, the intervals where the graph is increasing appear to be between $(- \infty, -18)$ and $(4, \infty)$.

2. Intervals where the graph is decreasing:

   • The graph is decreasing between the x-values where the slope is negative. Based on the graph, the decreasing intervals are between $(-18, 4)$.

3. Relative Maximum Values:

   • The relative maximum value occurs at a local high point of the graph. Based on the graph, the relative maximum is 4 (located at the peak).

4. Relative Minimum Values:

   • The relative minimum occurs at a local low point of the graph. From the image, the relative minimum value appears to be -4 (located at the trough).

5. Domain:

   • The domain is the set of all x-values for which the function is defined. Based on the graph, it seems the domain is all real numbers, so the domain is $(-\infty, \infty)$.

6. Range:

   • The range is the set of all possible output (y) values. Based on the graph, the range appears to be $[-4, \infty)$.

Would you like any further clarification or more details on any of these steps? Let me know if you have additional questions!

Here are five related questions that could expand on the concepts:

1. How can we determine the concavity of the graph from its shape?
2. What does the first derivative of the function tell us about the graph?
3. How would you find the critical points of the graph algebraically?
4. How do we interpret the inflection points of the graph?
5. What does the second derivative test indicate about the relative extrema of a function?

Tip: When identifying intervals where the graph is increasing or decreasing, focus on the behavior of the slope (whether it is positive or negative) in the different regions of the graph.