A rational function is a function of the form
On the graph restricted values of an axis form a straight line, called asymptote, which cannot be crossed by the function. If zeros of numerator and denominator are equal, then the function is a horizontal line with the hole on a restricted value of x.
Let's see an example of in a factored form: . Obviously, roots of denominator is -5 and 4. That is, if x takes one of these two values, the denominator becomes equal to zero. Since the division by zero is impossible, the function is not defined or discontinuous at x = -5 and x = 4.
The function is continuous at all other values for x. The domain (area of acceptable values) for the function, as expressed in interval notation, is: