🏷️ LIMITED TIME OFFER: GET 20% OFF GRADE+ YEARLY SUBSCRIPTION →

HomeClass Notes1,200,000US530,000

MATH 041 Lecture Notes - Lecture 10: Asymptote

39 views3 pages

amaranthhornet495

5 Oct 2016

School

Department

Course

Professor

Mr.Terry M.Blakney

For unlimited access to Class Notes, a Class+ subscription is required.

Document Summary

Rational function r(x) = n(x)/d(x) ratio of two polynomial functions. R(x) = anx n + an-1x n-1 a1x + a0 bmxm + bm-1xm-1 b1x + b0. Ex #1: f(x) = x/(x-1) graph as we approach +1 from either direction? recall domain x 1, but what happens to the. Ex #2: f(x) = x 2 9 x + 3 domain x 3 f(x) = (x + 3)(x 3) = x 3 x -3 x + 3. The line y = b is a h. a. of f(x) if and only if f(x) approaches b as x approaches positive or negative . Given: f(x) = anx n + an-1x n-1 a1x + a0 bmxm + bm-1xm-1 b1x + b0. Look at n degree of numerator. Look at m degree of denominator. If n < m: the x-axis y=0 is the h. a. If n = m: the h. a. is the line y = an/bm. If n > m: then there is no h. a.

Related textbook solutions

Calculus

ISBN: 9781319050733

Single Variable Calculus: Early Transcendentals

4th Edition, 2018

ISBN: 9781337687805

CALCULUS:EARLY TRANSCENDENTALS

ISBN: 9781319050740

Related Documents

MATH 041 Lecture Notes - Lecture 9: Quadratic Formula, Coefficient

amaranthhornet495

MTH 107 Study Guide - Quiz Guide: Real Number, Even And Odd Functions, Precalculus

MATH-149 Midterm: MATH 147 Boise State Exam 1

turquoisegnu128

Related Questions

Algebra

Complete the sentence below. If r is a real zero of even multiplicity of a function f then the graph of f the x-axis at r. If r is a real zero of even multiplicity of a function f then the graph of f the x-axis at r. Complete the sentence below. The graphs of power functions of the form f(x) = x n: where n is an even integer, always contain the points and The graphs of power functions of the form f(x) = x n: where n is an even integer, always contain the points and If r is a solution to the equation f(x) = 05 name three additional statements that can be made about f and r assuming f is a polynomial function. Choose the correct answer below. If r is a solution to the equation f(x) = 0, then r is a real zero of the polynomial function r is an x-intercept of the graph of and x - r is a factor of f. If r is a solution to the equation f(x) = 0, then r is a complex zero of the polynomial function r is an x-intercept of the graph of and x + r is a factor of f. If r is a solution to the equation f(x) = 0, then r is a real zero of the polynomial function r is a y-intercept of the graph of x and x + r is a factor of f. Explain what the notation Km f(x) = -infinity means. x rightarrow infinity Choose the correct answer below. The limit of f(x) as x approaches - infinity equals infinity. The limit of x as f(x) approaches infinity equals - infinity. The limit of f(x) as x approaches infinity equals - infinity. The limit of x as f(x) approaches - infinity equals infinity. Form a polynomial whose zeros and degree are given. Zeros: -7, multiplicity 1; - 3, multiplicity 2; degree 3 Type a polynomial with integer coefficients and a leading coefficient of 1 in the box below. F(x) = Find the vertical horizontal and oblique asymptotes, if any, for the following rational function.R(x) = 12x / x + 20 Select the correct choice below and fill in any answer boxes within your choice. The vertical asymptote(s) is/are x = (Use a comma to separate answers as needed.) There is no vertical asymptote. Find the vertical, horizontal and oblique asymptotes, if any, of the given rational function. R(x) = x3 - 64 / x2 - 6x + 8 Find the vertical asymptote(s), if any, of the function. Select the correct choice below and fill in any answer boxes within your choice. The vertical asymptote(s) is/are x = (Simplify your answer. Use a comma to separate answers as needed.) There is no vertical asymptote. Find the vertical, horizontal and oblique asymptotes, if any, for the given rational function. Q(x) = 2x2 - 7x - 4 / 3x2 - 7x - 20 Select the correct choice below and fill in any answer boxes within your choice. The vertical asymptote(s) is/are x = (Use a comma to separate answers as needed. Use integers or fractions for any numbers in the expression.) There is no vertical asymptote. Analyze the graph of the function. R(x) = x + 14 / x(x + 15) What is the domain of R(x)? {x x 0 andx - 16} {x x 0 andx - 16 andx - 14} {x x 0 and x - 14} All real numbers Analyze the graph of the function. R(x) = 5x + 5 / 4x + 12 What is the domain of R(x)? {x|x 0 and x -3 and x - 1} {x|x -3} {x|x and x - 3} All real numbers Analyze the graph of the function.R(x) = x2 / x2 + x - 56 What is the domain of R(x)? {x|x 7 and x - 8} {x|x 0,x -1, and x 8} {x|x 0, x 7, and x - 8} All real numbers

Show transcribed image text Complete the sentence below. If r is a real zero of even multiplicity of a function f then the graph of f the x-axis at r. If r is a real zero of even multiplicity of a function f then the graph of f the x-axis at r. Complete the sentence below. The graphs of power functions of the form f(x) = x n: where n is an even integer, always contain the points and The graphs of power functions of the form f(x) = x n: where n is an even integer, always contain the points and If r is a solution to the equation f(x) = 05 name three additional statements that can be made about f and r assuming f is a polynomial function. Choose the correct answer below. If r is a solution to the equation f(x) = 0, then r is a real zero of the polynomial function r is an x-intercept of the graph of and x - r is a factor of f. If r is a solution to the equation f(x) = 0, then r is a complex zero of the polynomial function r is an x-intercept of the graph of and x + r is a factor of f. If r is a solution to the equation f(x) = 0, then r is a real zero of the polynomial function r is a y-intercept of the graph of x and x + r is a factor of f. Explain what the notation Km f(x) = -infinity means. x rightarrow infinity Choose the correct answer below. The limit of f(x) as x approaches - infinity equals infinity. The limit of x as f(x) approaches infinity equals - infinity. The limit of f(x) as x approaches infinity equals - infinity. The limit of x as f(x) approaches - infinity equals infinity. Form a polynomial whose zeros and degree are given. Zeros: -7, multiplicity 1; - 3, multiplicity 2; degree 3 Type a polynomial with integer coefficients and a leading coefficient of 1 in the box below. F(x) = Find the vertical horizontal and oblique asymptotes, if any, for the following rational function.R(x) = 12x / x + 20 Select the correct choice below and fill in any answer boxes within your choice. The vertical asymptote(s) is/are x = (Use a comma to separate answers as needed.) There is no vertical asymptote. Find the vertical, horizontal and oblique asymptotes, if any, of the given rational function. R(x) = x3 - 64 / x2 - 6x + 8 Find the vertical asymptote(s), if any, of the function. Select the correct choice below and fill in any answer boxes within your choice. The vertical asymptote(s) is/are x = (Simplify your answer. Use a comma to separate answers as needed.) There is no vertical asymptote. Find the vertical, horizontal and oblique asymptotes, if any, for the given rational function. Q(x) = 2x2 - 7x - 4 / 3x2 - 7x - 20 Select the correct choice below and fill in any answer boxes within your choice. The vertical asymptote(s) is/are x = (Use a comma to separate answers as needed. Use integers or fractions for any numbers in the expression.) There is no vertical asymptote. Analyze the graph of the function. R(x) = x + 14 / x(x + 15) What is the domain of R(x)? {x x 0 andx - 16} {x x 0 andx - 16 andx - 14} {x x 0 and x - 14} All real numbers Analyze the graph of the function. R(x) = 5x + 5 / 4x + 12 What is the domain of R(x)? {x|x 0 and x -3 and x - 1} {x|x -3} {x|x and x - 3} All real numbers Analyze the graph of the function.R(x) = x2 / x2 + x - 56 What is the domain of R(x)? {x|x 7 and x - 8} {x|x 0,x -1, and x 8} {x|x 0, x 7, and x - 8} All real numbers

indigosardine988

Algebra

Which rational function has the given graph? R(x) = 2x2/x2-4 R(x) = 2x2/x2+4 R(x) = -2x2/x2+4 R(x) = 2x2/x2+4 (R(x) = -2x2/x2-4 Use a transformation of the graph of y = x5 to graph the function. h(x) = -4x5 Choose the correct graph below. Determine whether the function is a polynomial function. If it is, state the degree. If it is not tell why not. g(x)= 1-x3/5 Choose the correct answer below. Polynomial of degree 3 Not a polynomial because of the negative coefficient of x3 Polynomial of degree 1 Not a polynomial because of the negative power of x Find the vertical, horizontal and oblique asymptotes, if any, of the given rational function. R(x) = x3 - 27/x2-x-6 Find the vertical asymptote(s), it any, of the function. Select the correct choice below and fill in any answer boxes within your choice. The vertical asymptote(s) is/are x = . (Simplify your answer. Use a comma to separate answers as needed.) There is no vertical asymptote. Find the horizontal asymptote(s), if any, of the function. Select the correct choice below and fill in any answer boxes within your choice. The horizontal asymptote(s) is/are y = . (Simplify your answer. Use a comma to separate answers as needed.) There is no horizontal asymptote. Find the oblique asymptote(s), if any, of the function. Select the correct choice below and fill in any answer boxes within your choice. The oblique asymptote(s) is/are y = . (Simplify your answer. Use a comma to separate answers as needed.) . There is no oblique asymptote. Use a transformation of the graph of y= x4 to graph the function. f(x) = (x+7)4 Find the vertical, horizontal and oblique asymptotes, if any, for the following rational function. R(x) = 8x/x+16 Select the correct choice below and till m any answer boxes within your choice. The vertical asymptote(s) is/are x = . (Use a comma to separate answers as needed.) There is no vertical asymptote. Select the correct choice below and fill in any answer boxes within your choice. The horizontal asymptote(s) is/are y = . (Use a comma to separate answers as needed.) There is no horizontal asymptote. Select the correct choice below and fill in any answer boxes within your choice. The oblique asymptote(s) is/are y = . (Use a comma to separate answers as needed.) There is no oblique asymptote. Which rational function could have the given graph? In the functions shown, c is a constant. Choose the correct answer below. R(x) = (x+1)2(x+4)(x+c)/(x-1)(x+3) R(x) = (x+1)(x+4)(x2+c)/(x-1)2(x+3)2 R(x) = (x+1)(x+4)2(x+c)/(x-1)(x+3) R(x) = (x+1)(x+4)(x2+c)/(x-1)2(x+3)2 Analyze the graph of the function. R(x) = x(x-9)2/(x+12)3 What is the domain of R(x)? {x|x 0, x 9, and x - 12} {x|x -12} {x|x 0 and x - 12} All real numbers What is the equation of the vertical asymptote(s) of R(x)? Select the correct choice below and fill in any answer boxes within your choice. x= (Use a comma to separate answers as needed. Type an integer or a fraction.) There is no vertical asymptote. What is the equation of the horizontal or oblique asymptote of R(x)? Select the correct choice below and fill in any answer boxes within your choice. y = (Simplify your answer.) There is no horizontal or oblique asymptote. Choose the correct graph for R(x) below. Find the vertical horizontal and oblique asymptotes, if any, for the following rational function. T(x) = x3/x4 - 1 Select the correct choice below and fill in any answer boxes within your choice. The vertical asymptote(s) is/are x = . (Use a comma to separate answers as needed.) There is no vertical asymptote. Select the correct choice below and fill in any answer boxes within your choice. The horizontal asymptote(s) is/are y = . (Use a comma to separate answers as needed.) There is no horizontal asymptote. Select the correct choice below and fill in any answer boxes within your choice. The oblique asymptote(s) is/are y= . (Use a comma to separate answers as needed.) There is no oblique asymptote.

Show transcribed image text Which rational function has the given graph? R(x) = 2x2/x2-4 R(x) = 2x2/x2+4 R(x) = -2x2/x2+4 R(x) = 2x2/x2+4 (R(x) = -2x2/x2-4 Use a transformation of the graph of y = x5 to graph the function. h(x) = -4x5 Choose the correct graph below. Determine whether the function is a polynomial function. If it is, state the degree. If it is not tell why not. g(x)= 1-x3/5 Choose the correct answer below. Polynomial of degree 3 Not a polynomial because of the negative coefficient of x3 Polynomial of degree 1 Not a polynomial because of the negative power of x Find the vertical, horizontal and oblique asymptotes, if any, of the given rational function. R(x) = x3 - 27/x2-x-6 Find the vertical asymptote(s), it any, of the function. Select the correct choice below and fill in any answer boxes within your choice. The vertical asymptote(s) is/are x = . (Simplify your answer. Use a comma to separate answers as needed.) There is no vertical asymptote. Find the horizontal asymptote(s), if any, of the function. Select the correct choice below and fill in any answer boxes within your choice. The horizontal asymptote(s) is/are y = . (Simplify your answer. Use a comma to separate answers as needed.) There is no horizontal asymptote. Find the oblique asymptote(s), if any, of the function. Select the correct choice below and fill in any answer boxes within your choice. The oblique asymptote(s) is/are y = . (Simplify your answer. Use a comma to separate answers as needed.) . There is no oblique asymptote. Use a transformation of the graph of y= x4 to graph the function. f(x) = (x+7)4 Find the vertical, horizontal and oblique asymptotes, if any, for the following rational function. R(x) = 8x/x+16 Select the correct choice below and till m any answer boxes within your choice. The vertical asymptote(s) is/are x = . (Use a comma to separate answers as needed.) There is no vertical asymptote. Select the correct choice below and fill in any answer boxes within your choice. The horizontal asymptote(s) is/are y = . (Use a comma to separate answers as needed.) There is no horizontal asymptote. Select the correct choice below and fill in any answer boxes within your choice. The oblique asymptote(s) is/are y = . (Use a comma to separate answers as needed.) There is no oblique asymptote. Which rational function could have the given graph? In the functions shown, c is a constant. Choose the correct answer below. R(x) = (x+1)2(x+4)(x+c)/(x-1)(x+3) R(x) = (x+1)(x+4)(x2+c)/(x-1)2(x+3)2 R(x) = (x+1)(x+4)2(x+c)/(x-1)(x+3) R(x) = (x+1)(x+4)(x2+c)/(x-1)2(x+3)2 Analyze the graph of the function. R(x) = x(x-9)2/(x+12)3 What is the domain of R(x)? {x|x 0, x 9, and x - 12} {x|x -12} {x|x 0 and x - 12} All real numbers What is the equation of the vertical asymptote(s) of R(x)? Select the correct choice below and fill in any answer boxes within your choice. x= (Use a comma to separate answers as needed. Type an integer or a fraction.) There is no vertical asymptote. What is the equation of the horizontal or oblique asymptote of R(x)? Select the correct choice below and fill in any answer boxes within your choice. y = (Simplify your answer.) There is no horizontal or oblique asymptote. Choose the correct graph for R(x) below. Find the vertical horizontal and oblique asymptotes, if any, for the following rational function. T(x) = x3/x4 - 1 Select the correct choice below and fill in any answer boxes within your choice. The vertical asymptote(s) is/are x = . (Use a comma to separate answers as needed.) There is no vertical asymptote. Select the correct choice below and fill in any answer boxes within your choice. The horizontal asymptote(s) is/are y = . (Use a comma to separate answers as needed.) There is no horizontal asymptote. Select the correct choice below and fill in any answer boxes within your choice. The oblique asymptote(s) is/are y= . (Use a comma to separate answers as needed.) There is no oblique asymptote.

What are the answers for all of these questions? I am confused on how to solve for these.

1.

2.

3.

4.

Show transcribed image text