What is a rational function?

Lessons

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

      $x$	-5	-4	-3	-2	-1	0	1	2	3	4	5
      $y = f\left( x \right) = \frac{1}{{x - 2}}$

   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.
      

      $x$	1.5	1.9	1.99	2	2.01	2.1	2.5
      $y = f\left( x \right) = \frac{1}{{x - 2}}$				undefined

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

      $x$	10	100	1000
      $y = f\left( x \right) = \frac{1}{{x - 2}}$

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

      $x$	-10	-100	-1000
      $y = f\left( x \right) = \frac{1}{{x - 2}}$