### Graph Analysis and Limits The image features a graph of the function \( g(x) \) plotted on a coordinate plane. The graph exhibits various behaviors such as oscillations, peaks, and asymptotes. #### Given Limits: - **(a)** \(\lim_{{x \to \infty}} g(x) = 2\) ✔️ - **(b)** \(\lim_{{x \to -\infty}} g(x) = -2\) ✔️ - **(c)** \(\lim_{{x \to 3}} g(x) = \text{infinity}\) ✔️ - **(d)** \(\lim_{{x \to 0}} g(x) =\) - **(e)** \(\lim_{{x \to 2^{+}}} g(x) =\) #### Asymptotes: **(f)** The equations of the asymptotes. (Select all that apply.) - [ ] \( x = -3 \) - [ ] \( x = -2 \) - [ ] \( x = 0 \) - [ ] \( x = 2 \) - [ ] \( x = 3 \) ### Graph Explanation: The graph shows the function \( g(x) \) with various key characteristics: 1. **Horizontal Behavior:** - As \( x \) approaches infinity, the function approaches a horizontal asymptote at \( y = 2 \). - As \( x \) approaches negative infinity, the function approaches another horizontal asymptote at \( y = -2 \). 2. **Vertical Asymptote:** - At \( x = 3 \), the graph shows a vertical asymptote as the limit approaches infinity. 3. **Unlabeled Points:** - The graph suggests potential vertical asymptotes at the points to evaluate in section (d) and (e), such as \( x = 0 \) and \( x = 2^+ \), but these are not explicitly solved in the provided options. This information can be used to interpret the behavior of the function \( g(x) \) as it approaches the specified points or extends toward infinity.
### Graph Analysis and Limits The image features a graph of the function \( g(x) \) plotted on a coordinate plane. The graph exhibits various behaviors such as oscillations, peaks, and asymptotes. #### Given Limits: - **(a)** \(\lim_{{x \to \infty}} g(x) = 2\) ✔️ - **(b)** \(\lim_{{x \to -\infty}} g(x) = -2\) ✔️ - **(c)** \(\lim_{{x \to 3}} g(x) = \text{infinity}\) ✔️ - **(d)** \(\lim_{{x \to 0}} g(x) =\) - **(e)** \(\lim_{{x \to 2^{+}}} g(x) =\) #### Asymptotes: **(f)** The equations of the asymptotes. (Select all that apply.) - [ ] \( x = -3 \) - [ ] \( x = -2 \) - [ ] \( x = 0 \) - [ ] \( x = 2 \) - [ ] \( x = 3 \) ### Graph Explanation: The graph shows the function \( g(x) \) with various key characteristics: 1. **Horizontal Behavior:** - As \( x \) approaches infinity, the function approaches a horizontal asymptote at \( y = 2 \). - As \( x \) approaches negative infinity, the function approaches another horizontal asymptote at \( y = -2 \). 2. **Vertical Asymptote:** - At \( x = 3 \), the graph shows a vertical asymptote as the limit approaches infinity. 3. **Unlabeled Points:** - The graph suggests potential vertical asymptotes at the points to evaluate in section (d) and (e), such as \( x = 0 \) and \( x = 2^+ \), but these are not explicitly solved in the provided options. This information can be used to interpret the behavior of the function \( g(x) \) as it approaches the specified points or extends toward infinity.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Graph Analysis and Limits
The image features a graph of the function \( g(x) \) plotted on a coordinate plane. The graph exhibits various behaviors such as oscillations, peaks, and asymptotes.
#### Given Limits:
- **(a)** \(\lim_{{x \to \infty}} g(x) = 2\) ✔️
- **(b)** \(\lim_{{x \to -\infty}} g(x) = -2\) ✔️
- **(c)** \(\lim_{{x \to 3}} g(x) = \text{infinity}\) ✔️
- **(d)** \(\lim_{{x \to 0}} g(x) =\)
- **(e)** \(\lim_{{x \to 2^{+}}} g(x) =\)
#### Asymptotes:
**(f)** The equations of the asymptotes. (Select all that apply.)
- [ ] \( x = -3 \)
- [ ] \( x = -2 \)
- [ ] \( x = 0 \)
- [ ] \( x = 2 \)
- [ ] \( x = 3 \)
### Graph Explanation:
The graph shows the function \( g(x) \) with various key characteristics:
1. **Horizontal Behavior:**
- As \( x \) approaches infinity, the function approaches a horizontal asymptote at \( y = 2 \).
- As \( x \) approaches negative infinity, the function approaches another horizontal asymptote at \( y = -2 \).
2. **Vertical Asymptote:**
- At \( x = 3 \), the graph shows a vertical asymptote as the limit approaches infinity.
3. **Unlabeled Points:**
- The graph suggests potential vertical asymptotes at the points to evaluate in section (d) and (e), such as \( x = 0 \) and \( x = 2^+ \), but these are not explicitly solved in the provided options.
This information can be used to interpret the behavior of the function \( g(x) \) as it approaches the specified points or extends toward infinity.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1e6ee9ac-917d-48ac-8e12-6329174ebdc0%2F3bf2effa-652d-4b71-b5b4-7daa63dfba34%2Fu9a2749.jpeg&w=3840&q=75)
Transcribed Image Text:### Graph Analysis and Limits
The image features a graph of the function \( g(x) \) plotted on a coordinate plane. The graph exhibits various behaviors such as oscillations, peaks, and asymptotes.
#### Given Limits:
- **(a)** \(\lim_{{x \to \infty}} g(x) = 2\) ✔️
- **(b)** \(\lim_{{x \to -\infty}} g(x) = -2\) ✔️
- **(c)** \(\lim_{{x \to 3}} g(x) = \text{infinity}\) ✔️
- **(d)** \(\lim_{{x \to 0}} g(x) =\)
- **(e)** \(\lim_{{x \to 2^{+}}} g(x) =\)
#### Asymptotes:
**(f)** The equations of the asymptotes. (Select all that apply.)
- [ ] \( x = -3 \)
- [ ] \( x = -2 \)
- [ ] \( x = 0 \)
- [ ] \( x = 2 \)
- [ ] \( x = 3 \)
### Graph Explanation:
The graph shows the function \( g(x) \) with various key characteristics:
1. **Horizontal Behavior:**
- As \( x \) approaches infinity, the function approaches a horizontal asymptote at \( y = 2 \).
- As \( x \) approaches negative infinity, the function approaches another horizontal asymptote at \( y = -2 \).
2. **Vertical Asymptote:**
- At \( x = 3 \), the graph shows a vertical asymptote as the limit approaches infinity.
3. **Unlabeled Points:**
- The graph suggests potential vertical asymptotes at the points to evaluate in section (d) and (e), such as \( x = 0 \) and \( x = 2^+ \), but these are not explicitly solved in the provided options.
This information can be used to interpret the behavior of the function \( g(x) \) as it approaches the specified points or extends toward infinity.
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