Explanation Procedure used: “To graph a rational function f ( x ) = p ( x ) q ( x ) , where p ( x ) and q ( x ) have no common factors other than constants: 1. Find any real zeros of the denominator. Determine the domain of the function and sketch any vertical asymptotes. 2. Find the horizontal asymptote or the oblique asymptote, if there is one, and sketch it. 3. Find any zeros of the function. The zeros are found by determining the zeros of the numerator. These are the first coordinates of the x -intercepts of the graph. 4. Find f ( 0 ) . This gives the y - intercept, ( 0 , f ( 0 ) ) , of the function. 5. Find other function values to determine the general shape. Then draw the graph.” Definition used: “For a rational function f ( x ) = p ( x ) q ( x ) , where p ( x ) and q ( x ) are polinomials with no common factors other than constants, if a is a zero of the denominator, then the line x = a is a vertical asymptote for the graph of the function.” “When the numerator and the denominator of a rational function have the same degree, the line y = a / b is the horizontal asymptote, where a and b are the leading coefficients of the numerator and the denominator, respectively. When the degree of the numerator of a rational function is less than the degree of the denominator, the x -axis, or y = 0 , is the horizontal asymptote. When the degree of the numerator of a rational function is greater than the degree of the denominator, there is no horizontal asymptote.” Calculation: The given function is f ( x ) = x + 1 x 2 + x − 6 . The equation f ( x ) = x + 1 x 2 + x − 6 can be written as, f ( x ) = x + 1 x 2 + x − 6 = x + 1 x 2 + 3 x − 2 x − 6 = x + 1 ( x + 3 ) ( x − 2 ) The numerator and denominator of the equation f ( x ) = x + 1 x 2 + x − 6 have no common factors To determine To check: The graph f ( x ) = x + 1 x 2 + x − 6 obtained in part (a), by using a graphing calculator.

College Algebra: Graphs and Models (6th Edition)

6th Edition

ISBN: 9780134179032

Author: Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen, Judith A. Penna

Publisher: PEARSON

See similar textbooks

Concept explainers

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, c…

Videos

Question

Chapter 4.5, Problem 76E

To determine

To draw: The hand drawn graph of the function f(x)=x+1x2+x−6 with all the asymptotes and list the domain, x-intercepts and y-intercepts.

To determine

To check: The graph f(x)=x+1x2+x−6 obtained in part (a), by using a graphing calculator.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.5, Problem 75E

Chapter 4.5, Problem 77E

Students have asked these similar questions

Identify the vertex of the graph of the function y = 2(x + 1)² -3

Use the graph of y = x2- 6x +9 to solve the equation x2- 6x = -9. Move A Undo A Redo x Reset 10 8 7 -2 -1 2 3 4 5 6 7 8 -2 -3 -4 9, 6. 5. 4. 3. 2. 1.

Determine algebraically whether the graph is symmetric with respect to the x-axis, the y-axis, and the origin. 2x =4y^2+ 4

Chapter 4 Solutions

College Algebra: Graphs and Models (6th Edition)

Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 2E Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 10E

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

To draw: The hand drawn graph of the function f ( x ) = x + 1 x 2 + x − 6 with all the asymptotes and list the domain, x -intercepts and y -intercepts.

Solution Summary: The author explains how to draw a hand drawn graph of the function f(x) with all the asymptotes and list the domain, x -intercepts and y