Graphs of rational functions

Examples
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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)=5x2−13x+6−2x2+3x+2g\left( x \right) = \frac{{5{x^2} - 13x + 6}}{{ - 2{x^2} + 3x + 2}}
    3. h(x)=x320x−100h\left( x \right) = \frac{{{x^3}}}{{20x - 100}}
  2. 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
  3. 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)=x−9x+9a(x) = \frac{x - 9}{x + 9}
    2. b(x)=x2−9x2+9b(x) = \frac{x^{2}-9}{x^{2}+9}
    3. c(x)=x2+9x2−9c(x) = \frac{x^{2}+9}{x^{2}-9}
    4. d(x)=x+9x2−9d(x) = \frac{x+9}{x^{2}-9}
    5. e(x)=x+3x2−9e(x) = \frac{x+3}{x^{2}-9}
    6. f(x)=x2+9x+9f(x) = \frac{x^{2}+9}{x+9}
    7. g(x)=−x−9−x2−9g(x) = \frac{-x-9}{-x^{2}-9}
    8. h(x)=−x2−9−x2+9h(x) = \frac{-x^{2}-9}{-x^{2}+9}
    9. i(x)=x2−9x+3i(x) = \frac{x^{2}-9}{x+3}
    10. j(x)=x3−9x2x2−3xj(x) = \frac{x^{3}-9x^{2}}{x^{2}-3x}