Explanation Procedure: “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 2 + x − 6 x 2 − x − 20 . The equation f ( x ) = x 2 + x − 6 x 2 − x − 20 can be written as, f ( x ) = x 2 + x − 6 x 2 − x − 20 = x 2 + 3 x − 2 x − 6 x 2 − 4 x − 5 x − 20 = ( x + 3 ) ( x − 2 ) ( x + 4 ) ( x − 5 ) The numerator and denominator of the equation f ( x ) = x 2 + x − 6 x 2 − x − 20 have no common factor

COLLEGE ALGEBRA: GRAPHS AND MODELS, LOOS

6th Edition

ISBN: 9780136175636

Author: BITTINGER

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 4, Problem 72RE

To determine

To graph: The function f(x)=x2+x−6x2−x−20 with all the asymptotes and list the domain, x-intercepts and y-intercepts.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4, Problem 71RE

Chapter 4, Problem 73RE

Students have asked these similar questions

stacie is a resident at a medical facility you work at. You are asked to chart the amount of solid food that she consumes.For the noon meal today, she ate 1/2 of a 3 ounce serving of meatloaf, 3/4 of her 3 ounce serving of mashed potatoes, and 1/3 of her 2 ounce serving of green beans. Show in decimal form how many ounces of solid food that Stacie consumed

I've been struggling with this because of how close the numbers are together!! I would really appreciate if someone could help me❤️

Matrix MЄ R4×4, as specified below, is an orthogonal matrix - thus, it fulfills MTM = I. M (ELES),- m2,1. We know also that all the six unknowns mr,c are non-negative with the exception of Your first task is to find the values of all the six unknowns. Think first, which of the mr,c you should find first. Next, consider a vector v = (-6, 0, 0, 8) T. What's the length of v, i.e., |v|? Using M as transformation matrix, map v onto w by w = Mv provide w with its numeric values. What's the length of w, especially when comparing it to the length of v? Finally, consider another vector p = ( 0, 0, 8, 6) T. What's the angle between v (from above) and p? Using M as transformation matrix, map p onto q by q = Mp - provide q with its numeric values. What's the angle between w and q, especially when comparing it to the angle between v and p?

Chapter 4 Solutions

COLLEGE ALGEBRA: GRAPHS AND MODELS, LOOS

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 graph: The function f ( x ) = x 2 + x − 6 x 2 − x − 20 with all the asymptotes and list the domain, x -intercepts and y -intercepts.

Solution Summary: The author explains how to graph a rational function with no common factors other than constants.

Videos

To graph: The function f(x)=x2+x−6x2−x−20 with all the asymptotes and list the domain, x-intercepts and y-intercepts.

Want to see the full answer?

Chapter 4 Solutions