To provide a complete response, I would need to see the specific graph or function you're referencing. Since I can't see the graph directly, I can guide you through the process of how to identify intercepts and describe the behavior of a function across intervals.
Here's how you can analyze the graph:
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Identify Intercepts:
- x-intercept(s): Points where the graph crosses the x-axis (where \(y = 0\)).
- y-intercept: The point where the graph crosses the y-axis (where \(x = 0\)).
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Analyze the intervals: For each interval, you would do the following:
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Between x = -2 and x = 3:
- Observe the slope of the graph in this interval. Is it going upwards (increasing), downwards (decreasing), or flat (constant)?
- Note the y-values (do they remain above the x-axis or below it? Are they positive or negative?).
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Between x = 3 and x = 5:
- Repeat the same analysis: determine whether the graph is increasing, decreasing, or constant, and identify the y-values.
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Between x = 5 and x = 7:
- Again, assess the behavior of the graph and the sign of the y-values.
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Between x = 7 and x = 10:
- Finally, analyze this interval for the same properties.
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After filling in your observations for each interval, you would complete statements such as:
- "Between x = -2 and x = 3, the function is ___ (increasing/decreasing/constant), and the y-values are ___ (positive/negative)."
- Continue in this format for the subsequent intervals.
If you provide me with more specific data or the general shape of the graph function's approach, I'd be able to assist further!