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
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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.
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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