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Find each key feature of the function shown in the graph. Enter all intervals using interval notation.
Enter the x-intercept as values of x only.

The graph with X-coordinate marks -4, -2, 0, 2, 4 and Y-coordinate mark -4, -2, -1, 0, 2 and 4. There are 3 key features. The first key feature has head at (0, 1) and tail at (-1, 0). The second key feature has head at (1, 0) and tail at (0, -1). The third key feature has head at (2, -1) and tail at (1, -2).

range =

domain =

x-intercept(s) =

average rate of change over the interval [0, 1] =

an interval where the graph is positive =

The graph shows three segments, and the key features are as follows:

1. **Range**: 
   The range refers to all possible \( y \)-values that the function can take. From the graph, the \( y \)-values range from \( -2 \) to \( 1 \). Therefore, the range is:
   \[
   [-2, 1]
   \]

2. **Domain**: 
   The domain refers to all possible \( x \)-values that the function can take. From the graph, the \( x \)-values range from \( -1 \) to \( 2 \). Therefore, the domain is:
   \[
   [-1, 2]
   \]

3. **X-intercepts**:
   The x-intercepts are the points where the graph crosses the \( x \)-axis. From the graph, the x-intercepts are at \( x = -1 \) and \( x = 1 \). Therefore, the x-intercepts are:
   \[
   x = -1, 1
   \]

4. **Average Rate of Change Over the Interval \([0, 1]\)**:
   The average rate of change is given by the formula:
   \[
   \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
   \]
   For the interval \([0, 1]\):
   - \( f(0) = 1 \)
   - \( f(1) = 0 \)
   Therefore, the average rate of change over \([0, 1]\) is:
   \[
   \frac{0 - 1}{1 - 0} = \frac{-1}{1} = -1
   \]

5. **An Interval Where the Graph Is Positive**:
   The graph is positive where the function is above the x-axis. From the graph, the interval where the function is positive is:
   \[
   (-1, 0)
   \]

If you have any questions or need further explanations, feel free to ask! 

Here are 5 related questions to deepen your understanding:
1. How do you determine the intervals where a function is increasing or decreasing?
2. What is the significance of the slope in determining the rate of change?
3. Can a function have more than one x-intercept? What does it mean?
4. How would you calculate the average rate of change over a different interval, such as \([1, 2]\)?
5. How do you find the y-intercept from a graph, and what does it represent?

**Tip**: Remember, the domain and range of a function provide crucial information about the limits of \( x \) and \( y \)-values, helping you understand the behavior of the function across its entire graph.

Explore the key features of a function from graph analysis including range, domain, x-intercepts, and average rate of change over an interval. Understand how to identify intervals where the graph is positive. Suitable for high school students.

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