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 x-intercept at a point (x, 0),
The y-intercept at a point (0, y),
Calculus contents A
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