**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.

Answered: Image /qna-images/answer/21c1d720-ccbb-4a3d-83d8-06e45d3be28a.jpg

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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Question

**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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