rational functions

A rational function is the quotient between two polynomials:

One of the simplest rational functions are the inverse proportionality functions, which have this algebraic expression:

Its graph is a hyperbola with its two branches in opposite quadrants and its asymptotes in the coordinates axes.

Its domain and its range is R-{0}, and it is an odd function. It is decreasing if k > 0, or increasing if   k < 0, in its domain. It has no extrema.

Examples:

Exercise: draw the graph of these functions:

 

 

 

 

 

 

 

Solutions:

a)

b)