https://file.aiquickdraw.com/mathbot/file/1730049956674een4dndz.jpg

Find intercepts, domain and range, intervals where decreasing, increasing or constant, determine whether even or odd or neither 

Let's analyze the graph to answer each part of your question. 

### 1. Intercepts
   - **X-intercepts**: Points where the graph crosses the x-axis. These are \((-1, 0)\) and \((1, 0)\).
   - **Y-intercept**: Point where the graph crosses the y-axis. This is \((0, 2)\).

### 2. Domain and Range
   - **Domain**: The x-values for which the function is defined. Observing the graph, the function exists from \(x = -3\) to \(x = 3\).  
     \[
     \text{Domain: } [-3, 3]
     \]
   - **Range**: The y-values that the function attains. From the graph, the lowest point is \(y = 0\) and the highest point is \(y = 3\).
     \[
     \text{Range: } [0, 3]
     \]

### 3. Intervals of Increase, Decrease, or Constant Behavior
   - **Increasing Intervals**: The graph is increasing in the following segments:
     - From \(x = -3\) to \(x = -1\)
     - From \(x = 1\) to \(x = 3\)
   - **Decreasing Intervals**: The graph is decreasing in the interval:
     - From \(x = -1\) to \(x = 1\)
   - **Constant Intervals**: There are no intervals where the graph remains constant.

### 4. Even, Odd, or Neither
   - **Even Function**: A function is even if it is symmetric with respect to the y-axis.
   - **Odd Function**: A function is odd if it is symmetric with respect to the origin.
   
   Observing the graph, it is symmetric about the y-axis, which means this function is **even**.

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Let me know if you would like more details on any part! Here are some related questions to consider:

1. How does symmetry affect the properties of even and odd functions?
2. What are some examples of functions that are neither even nor odd?
3. How can we find intercepts algebraically if given a function’s equation?
4. Why is it important to know the intervals of increase and decrease?
5. How does the range of a function affect its graph?

**Tip:** When analyzing graphs, always check for symmetry to help determine if a function is even, odd, or neither!

Find intercepts, domain and range, intervals where decreasing, increasing or constant, determine whether even or odd or neither.

Understand how to find intercepts, domain, and range of a function, determine intervals of increase or decrease, and analyze symmetry to identify if the function is even, odd, or neither. This problem focuses on key geometry and algebra concepts, suitable for students in Grades 9-11.

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