Slant asymptote

Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.

Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

Get the most by viewing this topic in your current grade. Pick your course now.

?
Intros
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 Existence of Slant Asymptotes

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

    1. a(x)=x2−3x−10x−5a(x) = \frac{x^{2} - 3x - 10}{x - 5}
    2. b(x)=x2−x−6x−5b(x) = \frac{x^{2} - x - 6}{x - 5}
    3. c(x)=5x3−7x2+10x+1c(x) = \frac{5x^{3} - 7x^{2} + 10}{x + 1}
  2. Determining the Equation of a Slant Asymptote Using Long Division

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

    1. b(x)=x2−x−6x−5b(x) = \frac{x^{2} - x - 6}{x - 5}
    2. p(x)=−9x2+x4x3−8p(x) = \frac{-9x^{2} + x^{4}}{x^{3} - 8}
  3. Determining the Equation of a Slant Asymptote Using Synthetic Division

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

    1. b(x)=x2−x−6x−5b(x) = \frac{x^{2} - x - 6}{x - 5}
    2. f(x)=x2+1x−3f(x) = \frac{x^{2} + 1}{x - 3}
  4. Graphing Rational Functions Incorporating All 3 Kinds of Asymptotes

    Sketch the rational function

    f(x)=2x2−x−6x+2f(x) = \frac{2x^{2} - x - 6}{x + 2}

    by determining:

    i) points of discontinuity

    ii) vertical asymptotes

    iii) horizontal asymptotes

    iv) slant asymptote

    Topic Notes
    ?
    When the polynomial in the numerator is exactly one degree higher than the polynomial in the denominator, there is a slant asymptote in the rational function. To determine the slant asymptote, we need to perform long division.

    For a simplified rational function, when the numerator is exactly one degree higher than the denominator, the rational function has a slant asymptote. To determine the equation of a slant asymptote, we perform long division.

    Basic Concepts
    ?
    Related Concepts
    ?