https://file.aiquickdraw.com/mathbot/file/17244196829840170kpmk.jpg

Give me the increase intervals , decreasing intervals , positive interval,negative intervals,X-intercept ,y intercept , average range , domain with set notation

Based on the image provided, I'll extract the details for the key features of the function as requested. The function appears to be a piecewise linear function depicted on a graph. Here's the information extracted:

### 1. **Increasing Intervals**: 
   The function is increasing where the graph slopes upwards.
   - Interval: \([2, 6]\)

### 2. **Decreasing Intervals**: 
   The function is decreasing where the graph slopes downwards.
   - Interval: \([-2, 2]\)

### 3. **Positive Intervals**: 
   The function is positive where the graph is above the x-axis.
   - Interval: \((0, 6]\)

### 4. **Negative Intervals**: 
   The function is negative where the graph is below the x-axis.
   - Interval: \([-2, 0)\)

### 5. **X-Intercepts**: 
   The x-values where the graph crosses the x-axis.
   - X-intercepts: \((0, 0)\) and \((6, 0)\)

### 6. **Y-Intercept**: 
   The y-value where the graph crosses the y-axis.
   - Y-intercept: \((0, 0)\)

### 7. **Domain (Set Notation)**: 
   All possible x-values for which the function is defined.
   - Domain: \([-2, 6]\)

### 8. **Range (Set Notation)**: 
   All possible y-values that the function can take.
   - Range: \([-3, 3]\)

### 9. **Average Rate of Change**:
   The average rate of change over an interval of the function is a measure of how much the function's output (y-value) changes per unit change in the input (x-value).
   - Interval: \([4, 6]\)
   - Average Rate of Change: \( \frac{0 - 3}{6 - 4} = -1.5 \)

Would you like further details or have any questions? Here are some related questions you might find interesting:

1. How do you determine the intervals of increase and decrease from a graph?
2. What does the average rate of change tell you about a function?
3. How does the domain and range of a function impact its graph?
4. Can a function have more than one x-intercept and y-intercept?
5. What is the significance of the positive and negative intervals of a function?

**Tip:** When analyzing a function graph, always pay close attention to where the graph crosses the axes, as these points provide critical information about the function's intercepts and intervals.

Explore the intervals of increase and decrease, positive and negative intervals, x-intercepts, y-intercept, domain, and range of a piecewise linear function with detailed graphical analysis. Suitable for students in Grades 9-12.

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