

Graphing rational
functions 
The
graph of the reciprocal
function, equilateral or rectangular hyperbola 
Translation of the reciprocal function, linear rational
function 
Graphs of rational
functions examples 





The
graphs of the rational functions 
·
Rational
functions  a ratio of two polynomials 



Reciprocal
function 



Translation of the reciprocal function,
called linear rational function. 



The
graph of the reciprocal
function, equilateral or rectangular hyperbola 
The
graph of the reciprocal function y =
1/x or y = k/x
is a rectangular (or
right) hyperbola of which asymptotes are the coordinate axes. 
If
k > 0
then, the function is decreasing from zero to negative infinity
and from positive infinity to zero, i.e., the graph of the
rectangular hyperbola opening in the first and third quadrants
as is shown in the right figure. 
The
vertices, 







Translation of the reciprocal function, linear rational
function 
The
rational function 

by
dividing the numerator by denominator, 

can
be rewritten into 

where, 


is
the constant, 

are
the vertical and the horizontal asymptote respectively. 

Therefore, the values of the vertical and the horizontal asymptotes
correspond to the coordinates of the horizontal and the
vertical translation of the reciprocal function y = k/x
as is shown in the figure
below.



Graphs of rational
functions, examples 
Example: Given
the rational function 

sketch
its graph. 

Solution:
The
vertical and the horizontal asymptote of the linear rational
function 




and the
coefficient 


The
xintercept
at a point (x,
0), 

The
yintercept
at a point (0,
y), 













Calculus
contents A 



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