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. (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): Horizontakasymptote(s): I (b) Find all x-intercepts and y-intercepts. Check all that apply. D -3 -6 O None intercept(s): O -6 O -2 D -3 I None intercept(s): (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 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. (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): Horizontakasymptote(s): I (b) Find all x-intercepts and y-intercepts. Check all that apply. D -3 -6 O None intercept(s): O -6 O -2 D -3 I None intercept(s): (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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![**Finding the Intercepts, Asymptotes, Domain, and Range from the Graph**
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.
### Graph Description
The graph features a rational function with visible vertical and horizontal asymptotes. The intersecting lines form a pattern typical of rational functions. Key points on the axes may indicate intercepts.
### 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):** [Input Box]
- **Horizontal asymptote(s):** [Input Box]
**(b)** Find all x-intercepts and y-intercepts. Check all that apply.
- **x-intercept(s):**
- [ ] -1
- [ ] -3
- [ ] -6
- [ ] None
- **y-intercept(s):**
- [ ] -6
- [ ] -2
- [ ] -3
- [ ] None
**(c)** Find the domain and range of \( f \). Write each answer as an interval or union of intervals.
- **Domain:** [Input Box]
- **Range:** [Input Box]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3899185f-2e74-4a69-b98e-bc78fbd80797%2Fb0de8ef2-45bd-43cf-9f1a-0b53c120f334%2Fqofcbag_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Finding the Intercepts, Asymptotes, Domain, and Range from the Graph**
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.
### Graph Description
The graph features a rational function with visible vertical and horizontal asymptotes. The intersecting lines form a pattern typical of rational functions. Key points on the axes may indicate intercepts.
### 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):** [Input Box]
- **Horizontal asymptote(s):** [Input Box]
**(b)** Find all x-intercepts and y-intercepts. Check all that apply.
- **x-intercept(s):**
- [ ] -1
- [ ] -3
- [ ] -6
- [ ] None
- **y-intercept(s):**
- [ ] -6
- [ ] -2
- [ ] -3
- [ ] None
**(c)** Find the domain and range of \( f \). Write each answer as an interval or union of intervals.
- **Domain:** [Input Box]
- **Range:** [Input Box]
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