Rational functions are functions in which the numerator and denominator are polynomials.

Since these functions have denominators, we must be concerned with excluding any numbers for which the denominator would be zero. 

What value(s) of x must be excluded from the domain of the function ? 

Since we know now that 4 must be excluded, what happens to the function about 4? Look at the tables of values on the left. 

It is obvious that the y-values grow without bound as x-values get closer to the excluded value 4. Compare this result with the graph of the function in window #4. (Note: The vertical line at x = 4 is not part of the graph.  This line can be removed if the graphing mode is changed from connected to dot, but I prefer to leave it as a reminder of the value that must be excluded from the domain.  This line is called the vertical asymptote. 
 

Graphing Calculator Explorations
What is the domain of the function ?  (Note: You will need to factor the denominator first.) Create a rational function that has an excluded domain value of x = -2.  Confirm your result by graphing. What is the excluded domain value of the function ?  What happens to the function for x-values close to this value?  Graph the function to verify your findings.