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To determine the absolute maximum of the function \( y = f(x) \) based on the graph you provided, we need to identify the highest point the curve reaches.

From the graph:

- The function passes through key points such as:
  - \( (-2, 1) \)
  - \( (0, 0) \)
  - \( (2, 6) \)
  - \( (4, 5) \)

The highest value of \( y \) appears at \( (2, 6) \), where the function reaches \( y = 6 \). Therefore, the **absolute maximum** occurs at \( x = 2 \), and the value of the absolute maximum is \( f(2) = 6 \).

Would you like more details or further clarification?

Here are five related questions you might want to explore:
1. What is the absolute minimum of the function \( y = f(x) \)?
2. How can we identify local maxima and minima from a graph?
3. What does it mean for a function to have a global maximum or minimum?
4. Can the absolute maximum change if we look beyond the provided interval?
5. How does the derivative help in identifying maximum and minimum points?

**Tip:** The absolute maximum or minimum can also be identified using the first and second derivative tests for continuous functions.

The absolute maximum of y=f(x) based on the graph.

Learn how to determine the absolute maximum of the function y=f(x) based on a graphical representation. This example covers key points such as maxima, minima, and critical points, suitable for high school students studying calculus and graph analysis.

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