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1. Find the vertical asymptotoes, horizontal asymptotes, and holes, if any, of the rational functions. If none, write "none." 3x + 5 (a) f(x) %3D x - 6 i. Give the domain of f(x). Domain: ii. Find any vertical asymptotes of f(x). iii. Find any horizontal asymptotes of f(x). y = iv. Find any holes of f(x). If any, give as a point. (x, y) =

1. Find the vertical asymptotoes, horizontal asymptotes, and holes, if any, of the rational functions. If none, write "none." 3x + 5 (a) f(x) %3D x - 6 i. Give the domain of f(x). Domain: ii. Find any vertical asymptotes of f(x). iii. Find any horizontal asymptotes of f(x). y = iv. Find any holes of f(x). If any, give as a point. (x, y) =

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Exercise: Analysis of Rational Functions** 1. Find the vertical asymptotes, horizontal asymptotes, and holes, if any, of the rational functions. If none, write "none." --- **(a) Function: \( f(x) = \frac{3x + 5}{x - 6} \)** i. **Give the domain of \( f(x) \).** **Domain:** _____________________ ii. **Find any vertical asymptotes of \( f(x) \).** \( x = \) _________________ iii. **Find any horizontal asymptotes of \( f(x) \).** \( y = \) _________________ iv. **Find any holes of \( f(x) \). If any, give as a point.** \( (x, y) = \) _____________________ --- **(b) Function: \( f(x) = \frac{x^2 + 6x + 5}{x^2 + 3x + 2} \)** i. **Give the domain of \( f(x) \).** **Domain:** _____________________ ii. **Find any vertical asymptotes of \( f(x) \). Hint: factor \( f(x) \).** \( x = \) _________________ iii. **Find any horizontal asymptotes of \( f(x) \), if any.** \( y = \) _________________ iv. **Find any holes of \( f(x) \). If any, give as a point.** \( (x, y) = \) _____________________ --- **(c) Function: \( f(x) = \frac{4x(x - 2)(x + 3)}{(x - 2)(x + 6)} \)** i. **Give the domain of \( f(x) \).** **Domain:** _____________________ ii. **Find any vertical asymptotes of \( f(x) \).** \( x = \) _________________ iii. **Find any horizontal asymptotes of \( f(x) \).** \( y = \) _________________ iv. **Find any holes of \( f(x) \). If any, give as a point.** \( (x, y) = \) _____________________ --- **Exercise Explanation:** This exercise
Transcribed Image Text:**Exercise: Analysis of Rational Functions** 1. Find the vertical asymptotes, horizontal asymptotes, and holes, if any, of the rational functions. If none, write "none." --- **(a) Function: \( f(x) = \frac{3x + 5}{x - 6} \)** i. **Give the domain of \( f(x) \).** **Domain:** _____________________ ii. **Find any vertical asymptotes of \( f(x) \).** \( x = \) _________________ iii. **Find any horizontal asymptotes of \( f(x) \).** \( y = \) _________________ iv. **Find any holes of \( f(x) \). If any, give as a point.** \( (x, y) = \) _____________________ --- **(b) Function: \( f(x) = \frac{x^2 + 6x + 5}{x^2 + 3x + 2} \)** i. **Give the domain of \( f(x) \).** **Domain:** _____________________ ii. **Find any vertical asymptotes of \( f(x) \). Hint: factor \( f(x) \).** \( x = \) _________________ iii. **Find any horizontal asymptotes of \( f(x) \), if any.** \( y = \) _________________ iv. **Find any holes of \( f(x) \). If any, give as a point.** \( (x, y) = \) _____________________ --- **(c) Function: \( f(x) = \frac{4x(x - 2)(x + 3)}{(x - 2)(x + 6)} \)** i. **Give the domain of \( f(x) \).** **Domain:** _____________________ ii. **Find any vertical asymptotes of \( f(x) \).** \( x = \) _________________ iii. **Find any horizontal asymptotes of \( f(x) \).** \( y = \) _________________ iv. **Find any holes of \( f(x) \). If any, give as a point.** \( (x, y) = \) _____________________ --- **Exercise Explanation:** This exercise
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