(a) Write the equations for all vertical and horizontal asymptotes. Enter the equations using the "and" butt necessary. Select "None" as necessary. Vertical asymptote(s): x = -4, x = 2 Horizontal asymptote(s): y = 0 (b) Find all x-intercepts and y-intercepts. Check all that ap X- Intercept(s): O-4 V -1 O 2 O Nor intercept(s): O -1 Non (c) Find the domain and range of f. Write each answer as an interval or union of intervals. Domain: (-0, -4) u (-4, 2) u (2, o)
(a) Write the equations for all vertical and horizontal asymptotes. Enter the equations using the "and" butt necessary. Select "None" as necessary. Vertical asymptote(s): x = -4, x = 2 Horizontal asymptote(s): y = 0 (b) Find all x-intercepts and y-intercepts. Check all that ap X- Intercept(s): O-4 V -1 O 2 O Nor intercept(s): O -1 Non (c) Find the domain and range of f. Write each answer as an interval or union of intervals. Domain: (-0, -4) u (-4, 2) u (2, o)
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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Question
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Range is incorrect
Transcribed Image Text:The image is part of an educational task on finding the intercepts, asymptotes, domain, and range of a rational function. The function's graph is shown, featuring vertical and horizontal asymptotes and intercepts.
### Graph Description:
The graph displays a typical rational function with the following features:
- **Vertical Asymptotes**: The lines \( x = -4 \) and \( x = 2 \).
- **Horizontal Asymptote**: The line \( y = 0 \).
- The graph consists of curves approaching the asymptotes, characteristic of rational functions.
### Instructions and Tasks:
(a) **Asymptotes**:
- Define equations for vertical and horizontal asymptotes:
- Vertical asymptotes: \( x = -4, x = 2 \).
- Horizontal asymptote: \( y = 0 \).
(b) **Intercepts**:
- Identify all \( x \)-intercepts and \( y \)-intercepts from options provided:
- \( x \)-intercept(s): -4, -1, 0, 2, None.
- \( y \)-intercept(s): -1, 0, 1, None.
(c) **Domain and Range**:
- Express the domain and range as intervals or unions of intervals:
- Domain: \( (-\infty, -4) \cup (-4, 2) \cup (2, \infty) \).
- Range: \( (-\infty, 0) \cup (0, \infty) \).
### Error Notification:
The current response is incorrect, particularly regarding the range.
### Interactive Component:
Options for explanation or rechecking the answer are available.
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