Graphs of rational functions

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 Practise With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practise 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!

0/14
?
Examples
Lessons
  1. Graphing Rational Functions

    Sketch each rational function by determining:

    i) vertical asymptote.

    ii) horizontal asymptotes

    1. f(x)=52x+10f\left( x \right) = \frac{5}{{2x + 10}}
    2. g(x)=5x213x+62x2+3x+2g\left( x \right) = \frac{{5{x^2} - 13x + 6}}{{ - 2{x^2} + 3x + 2}}
    3. h(x)=x320x100h\left( x \right) = \frac{{{x^3}}}{{20x - 100}}
  2. Graphing Rational Functions Incorporating All 3 Kinds of Asymptotes

    Sketch the rational function

    f(x)=2x2x6x+2f(x) = \frac{2x^{2}-x-6}{x+2}

    by determining:

    i) points of discontinuity
    ii) vertical asymptotes
    iii) horizontal asymptotes
    iv) slant asymptote
    1. Identifying Characteristics of Rational Functions

      Without sketching the graph, determine the following features for each rational function:

      i) point of discontinuity

      ii) vertical asymptote

      iii) horizontal asymptote

      iv) slant asymptote

      1. a(x)=x9x+9a(x) = \frac{x - 9}{x + 9}
      2. b(x)=x29x2+9b(x) = \frac{x^{2}-9}{x^{2}+9}
      3. c(x)=x2+9x29c(x) = \frac{x^{2}+9}{x^{2}-9}
      4. d(x)=x+9x29d(x) = \frac{x+9}{x^{2}-9}
      5. e(x)=x+3x29e(x) = \frac{x+3}{x^{2}-9}
      6. f(x)=x2+9x+9f(x) = \frac{x^{2}+9}{x+9}
      7. g(x)=x9x29g(x) = \frac{-x-9}{-x^{2}-9}
      8. h(x)=x29x2+9h(x) = \frac{-x^{2}-9}{-x^{2}+9}
      9. i(x)=x29x+3i(x) = \frac{x^{2}-9}{x+3}
      10. j(x)=x39x2x23xj(x) = \frac{x^{3}-9x^{2}}{x^{2}-3x}
    Topic Notes
    ?