how to find slant asymptotes using synthetic division

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Slant asymptote

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Introduction

Lessons

1. Introduction to slant asymptote

   i) What is a slant asymptote?

   ii) When does a slant asymptote occur?

   iii) Overview: Slant asymptote

Examples

Lessons

1. Algebraically Determining the Being of Slant Asymptotes

   Without sketching the graph of the function, determine whether or not each function has a camber asymptote:

   1. $a(x) = \frac{10^{two} - 3x - 10}{10 - 5}$
   2. $b(x) = \frac{x^{2} - x - half-dozen}{x - 5}$
   3. $c(x) = \frac{5x^{three} - 7x^{2} + 10}{x + 1}$
2. Determining the Equation of a Slant Asymptote Using Long Partitioning

   Decide the equations of the slant asymptotes for the post-obit functions using long division.

   1. $b(x) = \frac{10^{2} - x - vi}{x - 5}$
   2. $p(x) = \frac{-9x^{2} + 10^{4}}{10^{3} - eight}$
3. Determining the Equation of a Camber Asymptote Using Synthetic Division

   Determine the equations of the slant asymptotes for the following functions using long division.

   1. $b(x) = \frac{ten^{2} - 10 - half-dozen}{ten - 5}$
   2. $f(x) = \frac{x^{ii} + 1}{x - iii}$
4. Graphing Rational Functions Incorporating All iii Kinds of Asymptotes

   Sketch the rational function

   $f(x) = \frac{2x^{two} - 10 - half dozen}{10 + 2}$

   by determining:

   i) points of aperture

   two) vertical asymptotes

   three) horizontal asymptotes

   iv) slant asymptote

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Topic Basics

When the polynomial in the numerator is exactly one degree college than the polynomial in the denominator, there is a camber asymptote in the rational role. To determine the camber asymptote, we need to perform long sectionalisation.

For a simplified rational part, when the numerator is exactly ane degree college than the denominator, the rational part has a slant asymptote. To determine the equation of a camber asymptote, we perform long division.

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