Intercepts? answer. Type an ordered pair. Use a in is. wer in interval notation.) ver in interval notation.) erval(s) is the graph increasing? Se h is increasing on r answer in interval notation. Use a is not increasing on any interval. s) is the graph decreasing? Select th s decreasing on answer in interval notation. Use a co = not decreasing on any interval.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Using the given graph of the function \( f \), find the following:

(a) the intercepts, if any  
(b) its domain and range  
(c) the intervals on which it is increasing, decreasing, or constant  
(d) whether it is even, odd, or neither  

---

(a) What are the intercepts?  
\[ \text{[      ]} \]  
(Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.)

(b) The domain is \[ \text{[      ]} \]  
(Type your answer in interval notation.)

The range is \[ \text{[      ]} \]  
(Type your answer in interval notation.)

(c) On which interval(s) is the graph increasing? Select the correct choice below and fill in any answer boxes within your choice.

- \( \text{A.} \) The graph is increasing on \[ \text{[      ]} \]  
  (Type your answer in interval notation. Use a comma to separate answers as needed.)

- \( \text{B.} \) The graph is not increasing on any interval.

On which interval(s) is the graph decreasing? Select the correct choice below and fill in any answer boxes within your choice.

- \( \text{A.} \) The graph is decreasing on \[ \text{[      ]} \]  
  (Type your answer in interval notation. Use a comma to separate answers as needed.)

- \( \text{B.} \) The graph is not decreasing on any interval.

On which interval(s) is the graph constant? Select the correct choice below and fill in any answer boxes within your choice.
Transcribed Image Text:Using the given graph of the function \( f \), find the following: (a) the intercepts, if any (b) its domain and range (c) the intervals on which it is increasing, decreasing, or constant (d) whether it is even, odd, or neither --- (a) What are the intercepts? \[ \text{[ ]} \] (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.) (b) The domain is \[ \text{[ ]} \] (Type your answer in interval notation.) The range is \[ \text{[ ]} \] (Type your answer in interval notation.) (c) On which interval(s) is the graph increasing? Select the correct choice below and fill in any answer boxes within your choice. - \( \text{A.} \) The graph is increasing on \[ \text{[ ]} \] (Type your answer in interval notation. Use a comma to separate answers as needed.) - \( \text{B.} \) The graph is not increasing on any interval. On which interval(s) is the graph decreasing? Select the correct choice below and fill in any answer boxes within your choice. - \( \text{A.} \) The graph is decreasing on \[ \text{[ ]} \] (Type your answer in interval notation. Use a comma to separate answers as needed.) - \( \text{B.} \) The graph is not decreasing on any interval. On which interval(s) is the graph constant? Select the correct choice below and fill in any answer boxes within your choice.
The image depicts a line graph on a coordinate plane with x and y axes. The graph's axes are labeled as \( x \) and \( y \), and the values range from -4 to 4 on both axes.

### Description of the Graph:

1. **Axes Details:**
   - The x-axis and y-axis intersect at the origin (0, 0).
   - Both axes feature a scale ranging from -4 to 4.

2. **Points and Line Segments:**
   - The graph consists of various line segments connecting points:
     - Begins at point (-4, 2).
     - Moves horizontally to point (-2, 2).
     - Descends diagonally to point (0, -2).
     - Continues downwards to point (2, -4).
     - Ascends diagonally to point (4, 0).

3. **Grid:**
   - The entire plane is covered with a square grid to facilitate precise plotting of points.
Transcribed Image Text:The image depicts a line graph on a coordinate plane with x and y axes. The graph's axes are labeled as \( x \) and \( y \), and the values range from -4 to 4 on both axes. ### Description of the Graph: 1. **Axes Details:** - The x-axis and y-axis intersect at the origin (0, 0). - Both axes feature a scale ranging from -4 to 4. 2. **Points and Line Segments:** - The graph consists of various line segments connecting points: - Begins at point (-4, 2). - Moves horizontally to point (-2, 2). - Descends diagonally to point (0, -2). - Continues downwards to point (2, -4). - Ascends diagonally to point (4, 0). 3. **Grid:** - The entire plane is covered with a square grid to facilitate precise plotting of points.
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