Based on the description of the graph, we are analyzing a function that has both open and closed points, which will help us determine the absolute and local maximum and minimum values.

Given Graph Description:

• Starts at an open point on the positive y-axis at $y = 5$.
• Ends at a closed point at $(7, 2)$.
• Key points:
  • Closed point at $(2, 2)$,
  • Local maximum at $(3, 4)$,
  • Local minimum at $(4, 1)$,
  • Turning point at $(6, 3)$.

Step-by-Step Analysis:

1. Absolute Maximum Value:
   • The absolute maximum is the highest $y$-value of the function over its entire domain.
   • From the description, the highest point is at $y = 5$ (open point on the y-axis).
   • However, because it is an open point (not included in the function), it is not considered a maximum.
   • The next highest point is at $y = 4$ at $(3, 4)$, which is a local maximum and a closed point.
   • Hence, the absolute maximum value is $\boxed{4}$.

Would you like more details on how to find the local extrema?

Here are 5 follow-up questions to explore:

1. What is the absolute minimum value of the function?
2. How do you identify local maxima and minima on a graph?
3. What is the difference between open and closed points on a function graph?
4. How do turning points affect the determination of maximum and minimum values?
5. Can a function have multiple absolute maxima or minima?

Tip: Always check whether the extreme values occur at closed points, as open points are not part of the graph's domain!