# Graphs of rational functions

### Graphs of rational functions

#### Lessons

• 1.
Graphing Rational Functions

Sketch each rational function by determining:

i) vertical asymptote.

ii) horizontal asymptotes

a)
$f\left( x \right) = \frac{5}{{2x + 10}}$

b)
$g\left( x \right) = \frac{{5{x^2} - 13x + 6}}{{ - 2{x^2} + 3x + 2}}$

c)
$h\left( x \right) = \frac{{{x^3}}}{{20x - 100}}$

• 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

a)
$a(x) = \frac{x - 9}{x + 9}$

b)
$b(x) = \frac{x^{2}-9}{x^{2}+9}$

c)
$c(x) = \frac{x^{2}+9}{x^{2}-9}$

d)
$d(x) = \frac{x+9}{x^{2}-9}$

e)
$e(x) = \frac{x+3}{x^{2}-9}$

f)
$f(x) = \frac{x^{2}+9}{x+9}$

g)
$g(x) = \frac{-x-9}{-x^{2}-9}$

h)
$h(x) = \frac{-x^{2}-9}{-x^{2}+9}$

i)
$i(x) = \frac{x^{2}-9}{x+3}$

j)
$j(x) = \frac{x^{3}-9x^{2}}{x^{2}-3x}$