Let's analyze the provided graph and information in the image to solve the questions.

Observations from the graph:

1. Relative Maximum: The highest point on the graph is at $( -5, 5 )$, so the function has a relative maximum of 5 at $x = -5$.
2. Relative Minimum: The lowest point on the graph is at $( 2, -4 )$, so the function has a relative minimum of -4 at $x = 2$.
3. Increasing Intervals: The function starts increasing after $x = 2$, so it is increasing on the interval $( 2, \infty )$.
4. Decreasing Intervals: The function decreases from $x = -\infty$ to $x = 2$, so it is decreasing on the interval $( -\infty, 2 )$.
5. Domain: The function is defined for all $x$ values, so the domain is $(-\infty, \infty)$.
6. Range: The lowest point is $-4$ (at $x = 2$) and the function goes up to infinity, so the range is $[-4, \infty)$.

Corrected Answers:

• Relative Maximum: 5 at $x = -5$.
• Relative Minimum: -4 at $x = 2$.
• Increasing Interval: $(2, \infty)$.
• Decreasing Interval: $(-\infty, 2)$.
• Domain: $(-\infty, \infty)$.
• Range: $[-4, \infty)$.

Let me know if you'd like further details or have any questions. Here are some related questions to deepen your understanding:

1. How do you determine whether a function is increasing or decreasing from its graph?
2. What is the significance of relative maximum and minimum points in calculus?
3. Can you explain how to find the domain and range of a more complex function?
4. How would you verify if a function has a global maximum or minimum, rather than just relative ones?
5. What role does the first and second derivative play in finding increasing and decreasing intervals?

Tip: Always check the behavior of a function at critical points (where the derivative is zero or undefined) to determine relative extrema and the direction of change.