What is a rational function?

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Examples
Lessons
  1. Investigating Asymptotes on the Graph of Rational Functions
    Consider the rational function f(x)=1x−2f\left( x \right) = \frac{1}{{x - 2}} .
    1. Complete the table of values below, then plot the points on the grid.

      xx

      -5

      -4

      -3

      -2

      -1

      0

      1

      2

      3

      4

      5

      y=f(x)=1x−2y = f\left( x \right) = \frac{1}{{x - 2}}

    2. What is the non-permissible value of the rational function?
    3. Now, let's investigate the behaviour of the rational function near the non-permissible value by plotting more points close to the non-permissible value.

      xx

      1.5

      1.9

      1.99

      2

      2.01

      2.1

      2.5

      y=f(x)=1x−2y = f\left( x \right) = \frac{1}{{x - 2}}

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    4. To investigate the right-end behaviour of the rational function (as x→∞x \to \infty ), complete the table of values below and plot the points.

      xx

      10

      100

      1000

      y=f(x)=1x−2y = f\left( x \right) = \frac{1}{{x - 2}}

    5. To investigate the left-end behaviour of the rational function (as x→−∞x \to - \infty ), complete the table of values below and plot the points.

      xx

      -10

      -100

      -1000

      y=f(x)=1x−2y = f\left( x \right) = \frac{1}{{x - 2}}

Topic Notes
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A rational function is defined as a "ratio" of polynomials: rational  function=polynomialpolynomialrational\;function = \frac{{polynomial}}{{polynomial}}
For example: f(x)=x3+5x2−8x+6x2−1f\left( x \right) = \frac{{{x^3} + 5{x^2} - 8x + 6}}{{{x^2} - 1}} ; g(x)=1x2−4g\left( x \right) = \frac{1}{{{x^2} - 4}} ; h(x)=−8x+32x−5h\left( x \right) = \frac{{ - 8x + 3}}{{2x - 5}}