# Graphs of rational functions

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##### Examples
###### 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
1. 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. $j(x) = \frac{x^{3}-9x^{2}}{x^{2}-3x}$