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Determine all Horizontal Asymptotes. x²-2x+1 x³+x-7 50. f(x)=. 51. f

Determine all Horizontal Asymptotes. x²-2x+1 x³+x-7 50. f(x)=. 51. f

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter5: A Survey Of Other Common Functions
Section5.6: Higher-degree Polynomials And Rational Functions
Problem 3TU
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Determine the horizontal asymptotes using the three cases below. Case I. Degree of the numerator is less than the degree of the denominator. The asymptote is y = 0. Example: y=- (As x becomes very large or very negative the value of this function will approach 0). Thus there is a horizontal asymptote at y=0. Case II. Degree of the numerator is the same as the degree of the denominator. The asymptote is the ratio of the lead coefficients. Exmaple: y=- 50. f(x)= HORIZONTAL ASYMPTOTES || Case III. Degree of the numerator is greater than the degree of the denominator. There is no horizontal asymptote. The function increases without bound. (If the degree of the numerator is exactly 1 more than the degree of the denominator, then there exists a slant asymptote, which is determined by long division.) Example: y = (As x becomes very large or very negative the value of this function will 2 approach 2/3). Thus there is a horizontal asymptote at y = -33. 53. f(x)=- 2x²+x-1 3x² +4 (2x-5)² x²-x Determine all Horizontal Asymptotes. x²–2x+1 x³+x-7 2x²+x-1 (As x becomes very large the value of the function will continue to increase 3x-3 and as x becomes very negative the value of the function will also become more negative). 5x³-2x² +8 4x-3x³ +5 51. f(x)=- *This is very important in the use of limits.* -3x+1 √x + x 54. f(x)=- 13 4x² 3x²-7 52. f(x)=- * Remember √x² = tx
Transcribed Image Text:Determine the horizontal asymptotes using the three cases below. Case I. Degree of the numerator is less than the degree of the denominator. The asymptote is y = 0. Example: y=- (As x becomes very large or very negative the value of this function will approach 0). Thus there is a horizontal asymptote at y=0. Case II. Degree of the numerator is the same as the degree of the denominator. The asymptote is the ratio of the lead coefficients. Exmaple: y=- 50. f(x)= HORIZONTAL ASYMPTOTES || Case III. Degree of the numerator is greater than the degree of the denominator. There is no horizontal asymptote. The function increases without bound. (If the degree of the numerator is exactly 1 more than the degree of the denominator, then there exists a slant asymptote, which is determined by long division.) Example: y = (As x becomes very large or very negative the value of this function will 2 approach 2/3). Thus there is a horizontal asymptote at y = -33. 53. f(x)=- 2x²+x-1 3x² +4 (2x-5)² x²-x Determine all Horizontal Asymptotes. x²–2x+1 x³+x-7 2x²+x-1 (As x becomes very large the value of the function will continue to increase 3x-3 and as x becomes very negative the value of the function will also become more negative). 5x³-2x² +8 4x-3x³ +5 51. f(x)=- *This is very important in the use of limits.* -3x+1 √x + x 54. f(x)=- 13 4x² 3x²-7 52. f(x)=- * Remember √x² = tx
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