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.