A rational function is defined as the quotient of polynomials in which the denominator has a degree of at least . In other words, there must be a variable in the denominator.The general form of a rational function is , where and are polynomials and .
The parent function of a rational function is and the graph is a hyperbola .
The domain and range is the set of all real numbers except .
In a rational function, an excluded value is any -value that makes the function value undefined. So, these values should be excluded from the domain of the function.
For example, the excluded value of the function is –3. That is, when , the value of is undefined.
So, the domain of this function is set of all real numbers except .
An asymptote is a line that the graph of the function approaches, but never touches. In the parent function , both the - and -axes are asymptotes. The graph of the parent function will get closer and closer to but never touches the asymptotes.
A rational function in the form has a vertical asymptote at the excluded value, or , and a horizontal asymptote at .
See also: Graphing Rational Functions