where N(x) and D(x) are polynomials and D(x) is not the zero polynomial.
Domain of a rational function of x is all real numbers except x-values that make the denominator zero.
Ex.
Domain:
Horizontal and Vertical Asymptotes
The line y = b is a horizontal asymptote of the graph of f if 
as 
or 
.
as or .Ex 1
The graph of
has the line y = -1 as a horizontal asymptote. The degree of the of the numerator is equal to the degree of the denominator, and the horizontal asymptote is given by the ratio of the leading coefficents of the numerator and denominator.
Ex 2
The graph of
has no horizontal asymptote because the degree of the numerator is greater than the degree of the denominator.
Ex 3
The graph of
has the line y=0 (the x-axis) as a horizontal asymptote. Note that the degree of the numerator is less than the degree of the denominator.
The line x = a is a vertical asymptote of the graph of f if or
as 
, either from the left or right.
Ex.
The graph of
has a vertical asymptote of 3 because that is where D(x) = 0.
Intercepts
Y-intercept :
X-Intercept(s):
or as , either from the left or right.Ex.
The graph of
has a vertical asymptote of 3 because that is where D(x) = 0.
Intercepts
Y-intercept :
X-Intercept(s):
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