Questions: Use the graph to determine (a) intervals on which the function is increasing, if any. (b) intervals on which the function is decreasing, if any. (c) intervals on which the function is constant, if any.

Use the graph to determine
(a) intervals on which the function is increasing, if any.
(b) intervals on which the function is decreasing, if any.
(c) intervals on which the function is constant, if any.
Transcript text: Use the graph to determine (a) intervals on which the function is increasing, if any. (b) intervals on which the function is decreasing, if any. (c) intervals on which the function is constant, if any.
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Solution

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Solution Steps

Step 1: Identify intervals where the function is increasing
  • The function is increasing where the graph moves upwards as we move from left to right.
  • From the graph, the function increases in the intervals \((-6, -4)\) and \((2, 4)\).
Step 2: Identify intervals where the function is decreasing
  • The function is decreasing where the graph moves downwards as we move from left to right.
  • From the graph, the function decreases in the intervals \((-4, 0)\) and \((4, 6)\).
Step 3: Identify intervals where the function is constant
  • The function is constant where the graph is a horizontal line.
  • From the graph, there are no intervals where the function is constant.

Final Answer

(a) Intervals on which the function is increasing: \((-6, -4)\) and \((2, 4)\)

(b) Intervals on which the function is decreasing: \((-4, 0)\) and \((4, 6)\)

(c) Intervals on which the function is constant: None

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