Graphs of rational functions

Graphs of rational functions

Lessons

  • 1.
    Graphing Rational Functions

    Sketch each rational function by determining:

    i) vertical asymptote.

    ii) horizontal asymptotes

    a)
    f(x)=52x+10f\left( x \right) = \frac{5}{{2x + 10}}

    b)
    g(x)=5x213x+62x2+3x+2g\left( x \right) = \frac{{5{x^2} - 13x + 6}}{{ - 2{x^2} + 3x + 2}}

    c)
    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

  • 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

    a)
    a(x)=x9x+9a(x) = \frac{x - 9}{x + 9}

    b)
    b(x)=x29x2+9b(x) = \frac{x^{2}-9}{x^{2}+9}

    c)
    c(x)=x2+9x29c(x) = \frac{x^{2}+9}{x^{2}-9}

    d)
    d(x)=x+9x29d(x) = \frac{x+9}{x^{2}-9}

    e)
    e(x)=x+3x29e(x) = \frac{x+3}{x^{2}-9}

    f)
    f(x)=x2+9x+9f(x) = \frac{x^{2}+9}{x+9}

    g)
    g(x)=x9x29g(x) = \frac{-x-9}{-x^{2}-9}

    h)
    h(x)=x29x2+9h(x) = \frac{-x^{2}-9}{-x^{2}+9}

    i)
    i(x)=x29x+3i(x) = \frac{x^{2}-9}{x+3}

    j)
    j(x)=x39x2x23xj(x) = \frac{x^{3}-9x^{2}}{x^{2}-3x}