12.6 What is a rational function?
What is a rational function?
Lessons
Notes:
A rational function is defined as a "ratio" of polynomials:
$rational\;function = \frac{{polynomial}}{{polynomial}}$
For example: $f\left( x \right) = \frac{{{x^3} + 5{x^2}  8x + 6}}{{{x^2}  1}}$ ; $g\left( x \right) = \frac{1}{{{x^2}  4}}$ ; $h\left( x \right) = \frac{{  8x + 3}}{{2x  5}}$

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 nonpermissible value of the rational function?

c)
c) Now, let’s investigate the behaviour of the rational function near the nonpermissible value by plotting more points close to the nonpermissible value.
$x$
1.5
1.9
1.99
2
2.01
2.1
2.5
$y = f\left( x \right) = \frac{1}{{x  2}}$
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d)
To investigate the rightend 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)
e) To investigate the leftend behaviour of the rational function (as $x \to  \infty$), complete the table of values below and plot the points.
$x$
10
100
1000
$y = f\left( x \right) = \frac{1}{{x  2}}$
