Graphs of rational functions

Lessons

1. Graphing Rational Functions

   Sketch each rational function by determining:

   i) vertical asymptote.

   ii) horizontal asymptotes

   1. $f\left( x \right) = \frac{5}{{2x + 10}}$
   2. $g\left( x \right) = \frac{{5{x^2} - 13x + 6}}{{ - 2{x^2} + 3x + 2}}$
   3. $h\left( x \right) = \frac{{{x^3}}}{{20x - 100}}$
2. Graphing Rational Functions Incorporating All 3 Kinds of Asymptotes

   Sketch the rational function

   $f(x) = \frac{2x^{2}-x-6}{x+2}$

   by determining:

   i) points of discontinuity
   ii) vertical asymptotes
   iii) horizontal asymptotes
   iv) slant asymptote
3. Identifying Characteristics of Rational Functions

   Without sketching the graph, determine the following features for each rational function:

   i) point of discontinuity

   ii) vertical asymptote

   iii) horizontal asymptote

   iv) slant asymptote

   1. $a(x) = \frac{x - 9}{x + 9}$
   2. $b(x) = \frac{x^{2}-9}{x^{2}+9}$
   3. $c(x) = \frac{x^{2}+9}{x^{2}-9}$
   4. $d(x) = \frac{x+9}{x^{2}-9}$
   5. $e(x) = \frac{x+3}{x^{2}-9}$
   6. $f(x) = \frac{x^{2}+9}{x+9}$
   7. $g(x) = \frac{-x-9}{-x^{2}-9}$
   8. $h(x) = \frac{-x^{2}-9}{-x^{2}+9}$
   9. $i(x) = \frac{x^{2}-9}{x+3}$
   10. $j(x) = \frac{x^{3}-9x^{2}}{x^{2}-3x}$