Homework Help is Here – Start Your Trial Now!
Math
Algebra
**Question 1** a. The equation of the horizontal asymptote for this function is \_\_\_\_ b. The equation of the vertical asymptote for this function is \_\_\_\_ Videos: [Q1] **Question 2** In the function formula \( f(x) = \frac{a}{x - p} + q \) \( p = \) \_\_\_\_ \( q = \) \_\_\_\_ **Transcription:** Consider the function \( f(x) = \frac{a}{x-p} + q \) where \( D \) is the x-intercept: \( \left( \frac{1}{3}, 0 \right) \). --- **Graph Explanation:** The graph is a hyperbola represented by the function \( f(x) = \frac{a}{x-p} + q \). It shows two branches in different quadrants. Below are the key features observed: - **Vertical Asymptote**: A dashed vertical line is present where the function is undefined, likely at \( x = p \). - **Horizontal Asymptote**: A dashed horizontal line represents the value that \( f(x) \) approaches as \( x \) tends to positive or negative infinity, likely at \( y = q \). - **X-Intercept**: The point \(\left( \frac{1}{3}, 0 \right)\) is marked on the x-axis, indicating where the graph crosses the x-axis. - The graph features an upward trend on one side of the vertical asymptote and a downward trend on the other. This is typically the behavior seen for rational functions of this form, which exhibit vertical and horizontal shifts based on the parameters \( p \) and \( q \).

**Question 1** a. The equation of the horizontal asymptote for this function is \_\_\_\_ b. The equation of the vertical asymptote for this function is \_\_\_\_ Videos: [Q1] **Question 2** In the function formula \( f(x) = \frac{a}{x - p} + q \) \( p = \) \_\_\_\_ \( q = \) \_\_\_\_ **Transcription:** Consider the function \( f(x) = \frac{a}{x-p} + q \) where \( D \) is the x-intercept: \( \left( \frac{1}{3}, 0 \right) \). --- **Graph Explanation:** The graph is a hyperbola represented by the function \( f(x) = \frac{a}{x-p} + q \). It shows two branches in different quadrants. Below are the key features observed: - **Vertical Asymptote**: A dashed vertical line is present where the function is undefined, likely at \( x = p \). - **Horizontal Asymptote**: A dashed horizontal line represents the value that \( f(x) \) approaches as \( x \) tends to positive or negative infinity, likely at \( y = q \). - **X-Intercept**: The point \(\left( \frac{1}{3}, 0 \right)\) is marked on the x-axis, indicating where the graph crosses the x-axis. - The graph features an upward trend on one side of the vertical asymptote and a downward trend on the other. This is typically the behavior seen for rational functions of this form, which exhibit vertical and horizontal shifts based on the parameters \( p \) and \( q \).

Algebra and Trigonometry (6th Edition)
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,...
See similar textbooks
icon
Related questions
Question
**Question 1** a. The equation of the horizontal asymptote for this function is \_\_\_\_ b. The equation of the vertical asymptote for this function is \_\_\_\_ Videos: [Q1] **Question 2** In the function formula \( f(x) = \frac{a}{x - p} + q \) \( p = \) \_\_\_\_ \( q = \) \_\_\_\_
Transcribed Image Text:**Question 1** a. The equation of the horizontal asymptote for this function is \_\_\_\_ b. The equation of the vertical asymptote for this function is \_\_\_\_ Videos: [Q1] **Question 2** In the function formula \( f(x) = \frac{a}{x - p} + q \) \( p = \) \_\_\_\_ \( q = \) \_\_\_\_
**Transcription:** Consider the function \( f(x) = \frac{a}{x-p} + q \) where \( D \) is the x-intercept: \( \left( \frac{1}{3}, 0 \right) \). --- **Graph Explanation:** The graph is a hyperbola represented by the function \( f(x) = \frac{a}{x-p} + q \). It shows two branches in different quadrants. Below are the key features observed: - **Vertical Asymptote**: A dashed vertical line is present where the function is undefined, likely at \( x = p \). - **Horizontal Asymptote**: A dashed horizontal line represents the value that \( f(x) \) approaches as \( x \) tends to positive or negative infinity, likely at \( y = q \). - **X-Intercept**: The point \(\left( \frac{1}{3}, 0 \right)\) is marked on the x-axis, indicating where the graph crosses the x-axis. - The graph features an upward trend on one side of the vertical asymptote and a downward trend on the other. This is typically the behavior seen for rational functions of this form, which exhibit vertical and horizontal shifts based on the parameters \( p \) and \( q \).
Transcribed Image Text:**Transcription:** Consider the function \( f(x) = \frac{a}{x-p} + q \) where \( D \) is the x-intercept: \( \left( \frac{1}{3}, 0 \right) \). --- **Graph Explanation:** The graph is a hyperbola represented by the function \( f(x) = \frac{a}{x-p} + q \). It shows two branches in different quadrants. Below are the key features observed: - **Vertical Asymptote**: A dashed vertical line is present where the function is undefined, likely at \( x = p \). - **Horizontal Asymptote**: A dashed horizontal line represents the value that \( f(x) \) approaches as \( x \) tends to positive or negative infinity, likely at \( y = q \). - **X-Intercept**: The point \(\left( \frac{1}{3}, 0 \right)\) is marked on the x-axis, indicating where the graph crosses the x-axis. - The graph features an upward trend on one side of the vertical asymptote and a downward trend on the other. This is typically the behavior seen for rational functions of this form, which exhibit vertical and horizontal shifts based on the parameters \( p \) and \( q \).
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS