The graph of a rational functionfis shown below. Assume that all asymptotes and intercepts are shown and that the graph has no "holes". Use the graph to complete the following. (a) Write the equations for all vertical and horizontal asymptotes. Enter the equations using the "and" button as necessary. Select "None" as necessary. Vertical asymptote(s): 8-+ Horizontal asymptote(s): U (b) Find all x-intercepts and y-intercepts. Check all that apply. X- intercept(s): O -4 O-1 O 2 None y- O-1 Intercept(s): None (c) Find the domain and range of f. Write each answer as an interval or union of intervals. Domain: Range:
The graph of a rational functionfis shown below. Assume that all asymptotes and intercepts are shown and that the graph has no "holes". Use the graph to complete the following. (a) Write the equations for all vertical and horizontal asymptotes. Enter the equations using the "and" button as necessary. Select "None" as necessary. Vertical asymptote(s): 8-+ Horizontal asymptote(s): U (b) Find all x-intercepts and y-intercepts. Check all that apply. X- intercept(s): O -4 O-1 O 2 None y- O-1 Intercept(s): None (c) Find the domain and range of f. Write each answer as an interval or union of intervals. Domain: Range:
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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![**Polynomial and Rational Functions: Finding the Intercepts, Asymptotes, Domain, and Range**
The graph of a rational function \( f \) is shown below. Assume that all asymptotes and intercepts are shown and that the graph has no "holes."
Use the graph to complete the following tasks:
(a) **Write the equations for all vertical and horizontal asymptotes.** Enter the equations using the “and” button as necessary. Select "None" as necessary.
- **Vertical asymptote(s):** [ ]
- **Horizontal asymptote(s):** [ ]
(b) **Find all x-intercepts and y-intercepts.** Check all that apply.
- **x-intercept(s):**
- [ ] \(-4\)
- [ ] \(-1\)
- [ ] \(2\)
- [ ] None
- **y-intercept(s):**
- [ ] \(-1\)
- [ ] \(0\)
- [ ] \(1\)
- [ ] None
(c) **Find the domain and range of \( f \).** Write each answer as an interval or union of intervals.
- **Domain:** [ ]
- **Range:** [ ]
**Explanation of the Graph:**
The graph displays a typical rational function with distinct vertical and horizontal asymptotes. Vertical dashed lines indicate the positions of the vertical asymptotes, while a horizontal dashed line represents the horizontal asymptote. The graph is drawn with smooth curves approaching but never touching these lines, depicting the function's behavior as it approaches infinity or negative infinity.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29ce3a4c-cb07-4c4c-bb91-a57b2d1f76d3%2Fba37fc15-7c6f-43b8-8d9b-41eeccabac33%2F9zvc83a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Polynomial and Rational Functions: Finding the Intercepts, Asymptotes, Domain, and Range**
The graph of a rational function \( f \) is shown below. Assume that all asymptotes and intercepts are shown and that the graph has no "holes."
Use the graph to complete the following tasks:
(a) **Write the equations for all vertical and horizontal asymptotes.** Enter the equations using the “and” button as necessary. Select "None" as necessary.
- **Vertical asymptote(s):** [ ]
- **Horizontal asymptote(s):** [ ]
(b) **Find all x-intercepts and y-intercepts.** Check all that apply.
- **x-intercept(s):**
- [ ] \(-4\)
- [ ] \(-1\)
- [ ] \(2\)
- [ ] None
- **y-intercept(s):**
- [ ] \(-1\)
- [ ] \(0\)
- [ ] \(1\)
- [ ] None
(c) **Find the domain and range of \( f \).** Write each answer as an interval or union of intervals.
- **Domain:** [ ]
- **Range:** [ ]
**Explanation of the Graph:**
The graph displays a typical rational function with distinct vertical and horizontal asymptotes. Vertical dashed lines indicate the positions of the vertical asymptotes, while a horizontal dashed line represents the horizontal asymptote. The graph is drawn with smooth curves approaching but never touching these lines, depicting the function's behavior as it approaches infinity or negative infinity.
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