What is a rational function?

Lessons

• 1.
  Investigating Asymptotes on the Graph of Rational Functions
  Consider the rational function $f\left( x \right) = \frac{1}{{x - 2}}$ .
  a)

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

  
  
  b)

  What is the non-permissible value of the rational function?
  
  
  c)

  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

  
  
  d)

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

  
  
  e)

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

  
  

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