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 2 − 9 x + 1 . The equation f ( x ) = x 2 − 9 x + 1 can be written as, f ( x ) = x 2 − 9 x + 1 = ( x + 3 ) ( x − 3 ) ( x + 1 ) The numerator and denominator of the equation f ( x ) = x 2 − 9 x + 1 have no common factor To determine To check: The graph f ( x ) = x 2 − 9 x + 1 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

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.

Videos

Question

Chapter 4.5, Problem 59E

To determine

To draw: The hand drawn graph of the function f(x)=x2−9x+1 with all the asymptotes and list the domain, x-intercepts and y-intercepts.

To determine

To check: The graph f(x)=x2−9x+1 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 58E

Chapter 4.5, Problem 60E

Students have asked these similar questions

America is getting older. The graph shows the projected elderly U.S. population for ages 65–84 and for ages 85 and older.The formula E = 5.8√x + 56.4 models the projected number of elderly Americans ages 65–84, E, in millions, x years after 2020.a. Use the formula to find the projected increase in the number of Americans ages 65–84, in millions, from 2030 to 2060. Express this difference in simplified radicalform.b. Use a calculator and write your answer in part (a) to the nearest tenth. Does this rounded decimal overestimate or underestimate the difference in the projected data shown by the bar graph ? By how much?

Marriage Rate The marriage rate per 1000 unmarried women for the years 1987–2014 is given by 132x + 1000y = 9570 where x is the number ofyears after 1980.a. Find the x-intercept of the graph of this function. b. Find and interpret the y-intercept of the graph ofthis function.c. Graph this function, using the intercepts.(Source: National Vital Statistics Report)

. Marriage Rate The marriage rate per 1000 unmarriedwomen for the years 1987–2014 can be modeled bythe function 132x + 1000y = 9570, where x is thenumber of years after 1980. During what year doesthe equation indicate the marriage rate will be 4.29?(Source: National Vital Statistics Report 2010)

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 2 − 9 x + 1 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