Determine whether the graph below is that of a function by using the vertical-line test. If it is, use the graph to find (a) its domain and range. (b) the intercepts, if any. (c) any symmetry with respect to the x-axis, y-axis, or the origin. Yes No A. The domain is [-, ]. The range is [-1, 1]. (Type your answers in interval notation.) OB. The graph is not a function. What are the intercepts? Select the correct choice below and fill in any answer boxes within your choice. - R OA. The intercepts are (Type an ordered pair. Type an exact answer using as needed. Use a comma to separate answers as needed.) OB. There are no intercepts. OC. The graph is not a function. -π/2 If the graph is that of a function, what are the domain and range of the function? Select the correct choice below and fill in any answer boxes within your choice. -1 π/2 π Q
Determine whether the graph below is that of a function by using the vertical-line test. If it is, use the graph to find (a) its domain and range. (b) the intercepts, if any. (c) any symmetry with respect to the x-axis, y-axis, or the origin. Yes No A. The domain is [-, ]. The range is [-1, 1]. (Type your answers in interval notation.) OB. The graph is not a function. What are the intercepts? Select the correct choice below and fill in any answer boxes within your choice. - R OA. The intercepts are (Type an ordered pair. Type an exact answer using as needed. Use a comma to separate answers as needed.) OB. There are no intercepts. OC. The graph is not a function. -π/2 If the graph is that of a function, what are the domain and range of the function? Select the correct choice below and fill in any answer boxes within your choice. -1 π/2 π Q
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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![### Determine Whether the Graph Represents a Function Using the Vertical Line Test
**Instructions:**
Using the graph provided, determine if it represents a function. If it does, use the graph to find:
1. Its domain and range.
2. The intercepts, if any.
3. Any symmetry with respect to the x-axis, y-axis, or the origin.
**Graph Analysis:**
- A graph is provided with labeled axes.
- The x-axis ranges from \(-\pi\) to \(\pi\).
- The y-axis ranges from -1 to 1.
- The graph shows a continuous curve passing through the origin, extending from \(-\pi\) to \(\pi\).
**Questions and Answers:**
1. **Is the graph a function?**
- ✅ Yes
- ⬜ No
2. **If the graph represents a function, determine the domain and range:**
- **Options:**
- ✅ A. The domain is \([-π, π]\). The range is \([-1, 1]\).
- ⬜ B. The graph is not a function.
3. **Identify the intercepts:**
- **Options:**
- ⬜ A. The intercepts are \([Enter values]\).
- *(Type an ordered pair. Use \(\pi\) as needed. Separate multiple answers with commas.)*
- ⬜ B. There are no intercepts.
- ⬜ C. The graph is not a function.
**Graph Details:**
- The graph depicted is symmetric with respect to the y-axis.
- The curve intercepts the origin at \((0, 0)\).
- The graph indicates potential x-intercepts at the points where it crosses the x-axis.
This demonstration helps in understanding the basic analysis of graphs concerning functions and symmetries.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf87f2e5-9dc6-40a8-a671-7dc06cda6841%2F67fdc788-0380-4718-92f6-8170c2e35213%2F55yvuyf_processed.png&w=3840&q=75)
Transcribed Image Text:### Determine Whether the Graph Represents a Function Using the Vertical Line Test
**Instructions:**
Using the graph provided, determine if it represents a function. If it does, use the graph to find:
1. Its domain and range.
2. The intercepts, if any.
3. Any symmetry with respect to the x-axis, y-axis, or the origin.
**Graph Analysis:**
- A graph is provided with labeled axes.
- The x-axis ranges from \(-\pi\) to \(\pi\).
- The y-axis ranges from -1 to 1.
- The graph shows a continuous curve passing through the origin, extending from \(-\pi\) to \(\pi\).
**Questions and Answers:**
1. **Is the graph a function?**
- ✅ Yes
- ⬜ No
2. **If the graph represents a function, determine the domain and range:**
- **Options:**
- ✅ A. The domain is \([-π, π]\). The range is \([-1, 1]\).
- ⬜ B. The graph is not a function.
3. **Identify the intercepts:**
- **Options:**
- ⬜ A. The intercepts are \([Enter values]\).
- *(Type an ordered pair. Use \(\pi\) as needed. Separate multiple answers with commas.)*
- ⬜ B. There are no intercepts.
- ⬜ C. The graph is not a function.
**Graph Details:**
- The graph depicted is symmetric with respect to the y-axis.
- The curve intercepts the origin at \((0, 0)\).
- The graph indicates potential x-intercepts at the points where it crosses the x-axis.
This demonstration helps in understanding the basic analysis of graphs concerning functions and symmetries.
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