in problems 49 - 56, for each graph of a function y = f(x), find the absolute maximum and the absolute…

Explanation:

Step1: Recall definitions

Absolute maximum is the highest (y - value) of the function over its entire domain, absolute minimum is the lowest (y - value). Local maximum is a point where the function value is greater than the values at nearby points, and local minimum is a point where the function value is less than the values at nearby points.

Step2: Analyze graph 49

• Absolute maximum: The highest (y - value) is (y = 4) at (x = 1), so the absolute maximum is (4).
• Absolute minimum: The lowest (y - value) is (y = 1) at (x = 5), so the absolute minimum is (1).
• Local maximum: At (x = 1,y = 4) and at (x = 3,y = 3) (since the function value is greater than nearby points).
• Local minimum: At (x = 2,y = 2) (since the function value is less than nearby points).

Answer:

For graph 49: Absolute maximum: (4) Absolute minimum: (1) Local maximum values: (4) (at (x = 1)) and (3) (at (x = 3)) Local minimum value: (2) (at (x = 2))

(Note: Since you didn't specify which graph to solve for among 49 - 56, I demonstrated the process for graph 49. If you want solutions for other graphs, please clarify).