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,...
Related questions
Question
Identify four ordered pairs on the graph of the function.
![### Understanding Rational Functions
The function displayed is:
\[ f(x) = \frac{x^2 + 10}{x^3 - 8} \]
### Exploring the Function
This is a rational function where:
- The **numerator** is \(x^2 + 10\).
- The **denominator** is \(x^3 - 8\).
### Key Elements of the Function
1. **Domain**: The function is undefined where the denominator is zero. Solve \(x^3 - 8 = 0\) to find these values.
2. **Asymptotes**:
- **Vertical Asymptotes**: Occur where the denominator is zero, provided the numerator does not also equal zero at these points.
- **Horizontal Asymptotes**: Determined by the degrees of the polynomials in the numerator and denominator.
3. **Intercepts**:
- **Y-intercept**: Set \(x = 0\) and solve for \(f(x)\).
- **X-intercepts**: Set the numerator equal to zero and solve for \(x\) (if possible).
### Graphing the Function
To understand the behavior of the graph:
- Identify any **asymptotes** and **intercepts**.
- Analyze the **end behavior** by considering the degrees of the numerator and denominator.
This information helps create a comprehensive graph of the function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fda625b26-af5c-4d40-b5ca-dba856450987%2F6fb584e8-1f06-4799-99d9-130516fa8da4%2F2dod6o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Rational Functions
The function displayed is:
\[ f(x) = \frac{x^2 + 10}{x^3 - 8} \]
### Exploring the Function
This is a rational function where:
- The **numerator** is \(x^2 + 10\).
- The **denominator** is \(x^3 - 8\).
### Key Elements of the Function
1. **Domain**: The function is undefined where the denominator is zero. Solve \(x^3 - 8 = 0\) to find these values.
2. **Asymptotes**:
- **Vertical Asymptotes**: Occur where the denominator is zero, provided the numerator does not also equal zero at these points.
- **Horizontal Asymptotes**: Determined by the degrees of the polynomials in the numerator and denominator.
3. **Intercepts**:
- **Y-intercept**: Set \(x = 0\) and solve for \(f(x)\).
- **X-intercepts**: Set the numerator equal to zero and solve for \(x\) (if possible).
### Graphing the Function
To understand the behavior of the graph:
- Identify any **asymptotes** and **intercepts**.
- Analyze the **end behavior** by considering the degrees of the numerator and denominator.
This information helps create a comprehensive graph of the function.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 1 images
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education