Questions: Find the open interval(s) where the following function is increasing, decreasing, or constant. Express your answer in interval notation.

Find the open interval(s) where the following function is increasing, decreasing, or constant. Express your answer in interval notation.
Transcript text: Find the open interval(s) where the following function is increasing, decreasing, or constant. Express your answer in interval notation.
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Solution

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Solution Steps

Step 1: Analyze the graph for increasing intervals

The function is increasing (going upwards from left to right) in two intervals. The first interval is from negative infinity up to x = -1, but not including -1 (since we're using open intervals). The second interval is from x = 2 to positive infinity, not including 2.

Step 2: Analyze the graph for decreasing intervals

The function is decreasing (going downwards from left to right) from x = -1 to x = 2, but not including -1 and 2.

Step 3: Express in interval notation

Increasing: (-∞, -1) and (2, ∞) Decreasing: (-1, 2)

Final Answer:

Increasing: (-∞, -1) and (2, ∞) Decreasing: (-1, 2) Constant: None

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