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The table you uploaded provides key features for graphing a function. Let's break down each feature and then sketch how the graph would look based on the provided details:

1. **Domain**: \((-4, 4)\)
   - The graph only exists between \(x = -4\) and \(x = 4\), so it won't extend beyond these values.

2. **Range**: \((-4, 6)\)
   - The graph's \(y\)-values range between \(y = -4\) and \(y = 6\), meaning the graph will reach from \(-4\) up to \(6\) vertically.

3. **Increasing Interval**: \((-4, 1)\)
   - The graph is increasing from \(x = -4\) to \(x = 1\), meaning it is rising as \(x\) moves from \(-4\) to \(1\).

4. **Decreasing Interval**: \((1, 4)\)
   - The graph is decreasing from \(x = 1\) to \(x = 4\), meaning it is falling as \(x\) moves from \(1\) to \(4\).

5. **X-Intercepts**: \((-2, 0)\) and \((3, 0)\)
   - The graph crosses the \(x\)-axis at \(x = -2\) and \(x = 3\).

6. **Y-Intercept**: \((0, 4)\)
   - The graph crosses the \(y\)-axis at \(y = 4\).

7. **Negative Interval**: \((-4, -2)\) and \((3, 4)\)
   - The graph is below the \(x\)-axis (negative \(y\)-values) between \(x = -4\) to \(x = -2\) and from \(x = 3\) to \(x = 4\).

8. **Positive Interval**: \((-2, 3)\)
   - The graph is above the \(x\)-axis (positive \(y\)-values) between \(x = -2\) and \(x = 3\).

### Step-by-Step Sketching Guide:
- The graph starts at \(x = -4\) and will be increasing until \(x = 1\), starting below the \(x\)-axis and crossing it at \(x = -2\).
- At \(x = 0\), the graph will be at \(y = 4\) (y-intercept).
- After reaching \(x = 1\), the graph will start decreasing until \(x = 4\), crossing the \(x\)-axis again at \(x = 3\).
- The graph will stay below the \(x\)-axis again from \(x = 3\) to \(x = 4\), while its maximum \(y\)-value is \(6\).

Would you like me to sketch this graph for you, or provide further details on any part? 

Here are some related questions you might consider:
1. How do increasing and decreasing intervals affect the shape of a graph?
2. What is the significance of the intercepts in a graph?
3. How can I determine concavity or inflection points from these features?
4. How would the graph change if the domain or range were different?
5. How do you plot the positive and negative intervals effectively?

**Tip**: Always start by plotting the intercepts (both \(x\)- and \(y\)-intercepts) as they are key points where the graph touches or crosses the axes.

Sketch a graph given the following key features: Domain: (-4,4), Range: (-4,6), Increasing: (-4,1), Decreasing (1,4), X-intercept: (-2,0), (3,0), Y-intercept: (0,4), Negative interval: (-4,-2) and (3,4), Positive interval: (-2,3)

Learn how to sketch a graph with defined domain, range, intervals of increase and decrease, and intercepts. This guide provides a step-by-step approach to graphing functions using key features like x and y intercepts, and positive and negative intervals. Suitable for high school students in grades 9-12.

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