5) Consider the following rational functions: -3x x²-4 Choose the graph of each function from the choices below: Graph B Graph A Graph D 5 -5 0 Which is the graph of f(x) = 12-x² f(x) = x²+x-6 12-x² x²+x-6 Which is the graph of g(x) = ? x². g(x) = Graph E Graph C 5 Hf H 0 5 Graph F -5 0
5) Consider the following rational functions: -3x x²-4 Choose the graph of each function from the choices below: Graph B Graph A Graph D 5 -5 0 Which is the graph of f(x) = 12-x² f(x) = x²+x-6 12-x² x²+x-6 Which is the graph of g(x) = ? x². g(x) = Graph E Graph C 5 Hf H 0 5 Graph F -5 0
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Problem 5: Rational Functions Graph Identification**
Consider the following rational functions:
\[ f(x) = \frac{12 - x^2}{x^2 + x - 6} \]
\[ g(x) = \frac{-3x}{x^2 - 4} \]
Choose the graph of each function from the choices below:
### Graphs:
- **Graph A**: Features a vertical asymptote and a hyperbolic shape opening upwards and downwards.
- **Graph B**: Shows a vertical asymptote and a hyperbolic shape, opening upwards and to the right.
- **Graph C**: Displays asymptotic behavior with sections opening upwards and downwards.
- **Graph D**: Exhibits a vertical asymptote with upward and leftward opening sections.
- **Graph E**: Shows asymptotic behavior with sections opening upwards and rightward.
- **Graph F**: Has a vertical asymptote and hyperbolic shape opening upwards and downwards.
### Questions:
- Which is the graph of \( f(x) = \frac{12-x^2}{x^2+x-6} \)? ___
- Which is the graph of \( g(x) = \frac{-3x}{x^2-4} \)? ___
**Instructions**: Analyze each graph to determine the correct match for each of the given rational functions by considering their asymptotic behaviors and intercepts.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F277ae00b-d056-42ed-a729-386f4fca5973%2F21c1d720-ccbb-4a3d-83d8-06e45d3be28a%2Fdotiw5h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 5: Rational Functions Graph Identification**
Consider the following rational functions:
\[ f(x) = \frac{12 - x^2}{x^2 + x - 6} \]
\[ g(x) = \frac{-3x}{x^2 - 4} \]
Choose the graph of each function from the choices below:
### Graphs:
- **Graph A**: Features a vertical asymptote and a hyperbolic shape opening upwards and downwards.
- **Graph B**: Shows a vertical asymptote and a hyperbolic shape, opening upwards and to the right.
- **Graph C**: Displays asymptotic behavior with sections opening upwards and downwards.
- **Graph D**: Exhibits a vertical asymptote with upward and leftward opening sections.
- **Graph E**: Shows asymptotic behavior with sections opening upwards and rightward.
- **Graph F**: Has a vertical asymptote and hyperbolic shape opening upwards and downwards.
### Questions:
- Which is the graph of \( f(x) = \frac{12-x^2}{x^2+x-6} \)? ___
- Which is the graph of \( g(x) = \frac{-3x}{x^2-4} \)? ___
**Instructions**: Analyze each graph to determine the correct match for each of the given rational functions by considering their asymptotic behaviors and intercepts.
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