Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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### Analysis of a Graphed Function

#### Graph Description:
The graph represents a function that features several critical points, where the slope of the function changes direction. 

- The x-axis ranges from -5 to 5.
- The y-axis ranges from -2 to 2.
- The function exhibits both increasing and decreasing behaviors as it moves from left to right.

#### Task:
Determine the intervals on which the function is increasing and decreasing. Provide your answers in open intervals.

#### Graph Analysis:
1. **Increasing Intervals:**
   - To identify the increasing intervals, observe where the function's values climb as you move from left to right.
   - From the graph, find segments where the curve rises.

2. **Decreasing Intervals:**
   - The decreasing intervals are where the function's values decline as you move from left to right.
   - Identify those areas on the graph where the curve dips.

#### Input Fields:
- **Increasing on the interval(s):**
  - Input the x-values denoting where the function is rising.
- **Decreasing on the interval(s):**
  - Input the x-values denoting where the function is falling.

**Note:** Your intervals should be presented as open intervals, meaning that the endpoints are not included.

### Example:
If the function is increasing from x = -4 to x = -1, this interval would be noted as (-4, -1).

### Your Answers:
- **Increasing on the interval(s):** [ _ ]
- **Decreasing on the interval(s):** [ _ ]

Ensure accuracy by inspecting the graph carefully and verifying where the function changes from increasing to decreasing and vice versa.
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Transcribed Image Text:### Analysis of a Graphed Function #### Graph Description: The graph represents a function that features several critical points, where the slope of the function changes direction. - The x-axis ranges from -5 to 5. - The y-axis ranges from -2 to 2. - The function exhibits both increasing and decreasing behaviors as it moves from left to right. #### Task: Determine the intervals on which the function is increasing and decreasing. Provide your answers in open intervals. #### Graph Analysis: 1. **Increasing Intervals:** - To identify the increasing intervals, observe where the function's values climb as you move from left to right. - From the graph, find segments where the curve rises. 2. **Decreasing Intervals:** - The decreasing intervals are where the function's values decline as you move from left to right. - Identify those areas on the graph where the curve dips. #### Input Fields: - **Increasing on the interval(s):** - Input the x-values denoting where the function is rising. - **Decreasing on the interval(s):** - Input the x-values denoting where the function is falling. **Note:** Your intervals should be presented as open intervals, meaning that the endpoints are not included. ### Example: If the function is increasing from x = -4 to x = -1, this interval would be noted as (-4, -1). ### Your Answers: - **Increasing on the interval(s):** [ _ ] - **Decreasing on the interval(s):** [ _ ] Ensure accuracy by inspecting the graph carefully and verifying where the function changes from increasing to decreasing and vice versa.
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