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Section 2.6 – Rational Functions

Section Details.
  • The definition of a rational function
  • Properties of a rational function such as the domain, \(x\)-intercepts, and \(y\)-intercepts
  • Determining the end behavior of a rational function and any horizontal asymptotes
  • Finding any vertical asymptotes and holes of a rational function


Practice Problems


Directions. The following are review problems for the section. We recommend you work the problems yourself, and then click "Answer" to check your answer. If you do not understand a problem, you can click "Video" to learn how to solve it. 
 
  1. Find the domain, holes, vertical asymptote(s), y-intercept, x-intercept(s), horizontal asymptote, and graph the following functions.
    1. \(f(x)=\cfrac{2x+5}{x+2}\)

      Domain: \((-\infty,-2)\cup(-2,\infty)\)
      Holes: None
      VA: \(x=-2\)
      y-int: \(\left(0,\dfrac{5}{2}\right)\)
      x-int: \(\left(-\dfrac{5}{2},0\right)\)
      HA: \(y=2\)

      Video Coming Soon!


    2. \(g(x)=\cfrac{6x^2-17x+5}{6x^2-13x-5}\)

      \(g(x)=\dfrac{(3x-1)(2x-5)}{(3x+1)(2x-5)}\)
      Domain: \(\left(-\infty, -\dfrac{1}{3}\right)\cup\left(-\dfrac{1}{3},\dfrac{5}{2}\right)\cup\left(\dfrac{5}{2},\infty\right)\)
      Holes: \(\left(\dfrac{5}{2},\dfrac{13}{17}\right)\)
      VA: \(x=-\dfrac{1}{3}\)
      y-int: \(\left(0,-1\right)\)
      x-int: \(\left(\dfrac{1}{3},0\right)\)
      HA: \(y=1\)


      To see the full video page and find related videos, click the following link.
      WIR3 20B M150 V13


  2. Find all intercepts, asymptotes, and holes of the following function.\[\displaystyle f(x)=\frac{x^2-11x+18}{x^2-5x+6}\]

    x-intercept: \((9,0)\)
    y-intercept: \((0,3)\)
    Vertical Asymptote: \(x=2\)
    Horizontal Asymptote: \(y=1\)
    Hole(s): \(\left(2,7\right)\)


    To see the full video page and find related videos, click the following link.
    WIR8 20B M150 V09