That is wrong because the first point points at (5,0) which is the maximum and then (7,0) as the minium and goes up to infinity 

Let's correct the analysis based on the new information:

1. **Maximum of the function**:
   - The graph shows a maximum at the point \((5, 0)\).
   - **Answer:** Maximum of 0 at \( x = 5 \).

2. **Minimum of the function**:
   - The graph shows a minimum at the point \((7, 0)\).
   - **Answer:** Minimum of 0 at \( x = 7 \).

3. **Intervals of Increase**:
   - The function increases from \( x = 7 \) to infinity.
   - **Answer:** Increasing on the interval \( (7, \infty) \).

4. **Intervals of Decrease**:
   - The function decreases between \( x = 5 \) and \( x = 7 \).
   - **Answer:** Decreasing on the interval \( (5, 7) \).

5. **Domain of the function**:
   - The graph covers all \( x \)-values from \( -\infty \) to \( \infty \), so the domain is all real numbers.
   - **Answer:** Domain is \( (-\infty, \infty) \).

6. **Range of the function**:
   - The lowest point on the graph is at \( y = 0 \), and the function increases without bound above that.
   - **Answer:** Range is \( [0, \infty) \).

Do you want more details or have any questions about this analysis?

### Related Questions:
1. How can you identify the maximum and minimum points on a graph?
2. Why is the function increasing after \( x = 7 \)?
3. What does it mean when a function has the same value at its maximum and minimum?
4. How does the domain of the function affect its behavior?
5. Why is the range of the function \( [0, \infty) \) and not just \( (0, \infty) \)?

**Tip:** Always carefully examine the points on the graph, particularly where the function changes direction, as these are often critical points that define maxima, minima, and intervals of increase or decrease.

Explore how to identify maximum and minimum points on a graph and analyze function behavior. This detailed analysis covers key concepts in calculus and graph theory, including the Extreme Value Theorem. Suitable for advanced high school students.

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