https://file.aiquickdraw.com/mathbot/file/17268421456549t5kreds.jpg

From the image, you have a function graph with specific points marked, and the task asks for several characteristics of this function.

Let's break down what we can infer and correct:

1. **Relative maximum:**
   - The relative maximum is **7** at \(x = 8\), which seems to be marked correctly.

2. **Relative minimum:**
   - The relative minimum is **-1** at \(x = 0\), and this is also correct.

3. **Function increasing/decreasing intervals:**
   - The function is **increasing** on intervals where the graph goes upward.
     - From the graph, the function starts increasing after the minimum point (which occurs at \(x = 0\)) until it reaches its maximum at \(x = 8\).
     - So, the function is increasing on the interval: \((0, 8)\).
     - The entered answer of \((-\infty, 0)\cup(8, \infty)\) is **incorrect** because it is not increasing from negative infinity to zero nor after \(x = 8\). The correct increasing interval should just be \((0, 8)\).

   - The function is **decreasing** where the graph slopes downward.
     - It starts decreasing from \(x = -\infty\) to the minimum at \(x = 0\). Hence, the function is decreasing on the interval \((-\infty, 0)\).

4. **Domain of the function:**
   - The domain is the set of all possible \(x\)-values that the function can take.
   - Since this is a continuous function without breaks, and the graph seems to extend infinitely in both directions horizontally, the domain is \((-\infty, \infty)\).

5. **Range of the function:**
   - The range is the set of all possible \(y\)-values the function takes.
   - The minimum value of the function is \(-1\) (at \(x = 0\)), and the maximum value is \(7\) (at \(x = 8\)).
   - Therefore, the range of the function is \([-1, 7]\).

### Corrections to be entered:
- **Increasing interval:** \((0, 8)\)
- **Domain:** \((-\infty, \infty)\)
- **Range:** \([-1, 7]\)

Would you like a detailed explanation for any of these concepts?

Here are five follow-up questions for practice:

1. What is the difference between absolute maximum/minimum and relative maximum/minimum?
2. How do you determine the intervals of increasing and decreasing on a graph?
3. What changes in the graph indicate a change from increasing to decreasing, or vice versa?
4. How does the behavior of the function at its endpoints influence its range?
5. Can a function have more than one relative maximum or minimum?

### Tip:
Always look for critical points on the graph where the slope changes sign (positive to negative or negative to positive) to determine maximum and minimum points.

Consider the function in the graph. The function has a relative maximum of 7 at x = 8. The function has a relative minimum of -1 at x = 0. Identify the intervals where the function is increasing and decreasing. Find the domain and range of the function.

This problem involves analyzing a function to find its relative maximum and minimum, determine its increasing and decreasing intervals, and identify the domain and range. Suitable for high school students studying calculus or precalculus.

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