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. -1/2 x/2 -1 Is the graph that of a function? O Yes
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. -1/2 x/2 -1 Is the graph that of a function? O Yes
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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A-c
![**Title: Understanding Functions Through Graph Analysis**
**Objective:**
Determine whether the graph below represents a function by using the vertical-line test. If it is a function, use the graph to identify:
a) Domain and Range
b) Intercepts, if any
c) Symmetry with respect to the x-axis, y-axis, or the origin
**Graph Description:**
The graph shown is a sine wave segment extending from \(-\pi\) to \(\pi\) on the x-axis and between -1 and 1 on the y-axis. It crosses the x-axis at \(-\pi\), \(0\), and \(\pi\), peaks at \(\frac{\pi}{2}\), and troughs at \(-\frac{\pi}{2}\).
**Questions:**
1. **Is the graph that of a function?**
- [ ] Yes
- [ ] No
2. **If the graph is that of a function, what are the domain and range of the function? Fill in the blanks using interval notation:**
- [ ] A. The domain is \(\_\_\_\_\). The range is \(\_\_\_\_\).
- [ ] B. The graph is not a function.
3. **What are the intercepts?** Select the correct choice below:
- [ ] \(x\)-intercepts at: \(\_\_\_\_\)
- [ ] \(y\)-intercept at: \(\_\_\_\_\)
**Note:** Use the dotted vertical line test to check if any vertical line intersects the graph at more than one point, determining if it's a function.
**Graph Symmetry:**
Determine any symmetry by analyzing the graph's reflection properties with respect to the x-axis, y-axis, or origin.
Click to select your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F323a188d-72c2-4f77-bbb3-3034e58495c9%2F6929012c-fde9-4e70-a408-841709ead360%2Fsqvbgw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Functions Through Graph Analysis**
**Objective:**
Determine whether the graph below represents a function by using the vertical-line test. If it is a function, use the graph to identify:
a) Domain and Range
b) Intercepts, if any
c) Symmetry with respect to the x-axis, y-axis, or the origin
**Graph Description:**
The graph shown is a sine wave segment extending from \(-\pi\) to \(\pi\) on the x-axis and between -1 and 1 on the y-axis. It crosses the x-axis at \(-\pi\), \(0\), and \(\pi\), peaks at \(\frac{\pi}{2}\), and troughs at \(-\frac{\pi}{2}\).
**Questions:**
1. **Is the graph that of a function?**
- [ ] Yes
- [ ] No
2. **If the graph is that of a function, what are the domain and range of the function? Fill in the blanks using interval notation:**
- [ ] A. The domain is \(\_\_\_\_\). The range is \(\_\_\_\_\).
- [ ] B. The graph is not a function.
3. **What are the intercepts?** Select the correct choice below:
- [ ] \(x\)-intercepts at: \(\_\_\_\_\)
- [ ] \(y\)-intercept at: \(\_\_\_\_\)
**Note:** Use the dotted vertical line test to check if any vertical line intersects the graph at more than one point, determining if it's a function.
**Graph Symmetry:**
Determine any symmetry by analyzing the graph's reflection properties with respect to the x-axis, y-axis, or origin.
Click to select your answer.
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