Vocabulary
Rational Function- A function of the form f(x)=p(x)/q(x) , P(x) and q(x) are polynomials and q(x)≠0.
Domain- The set of input values of a relation.
Range- The input values of a relation.
Asymptote- A line that a graph approaches more and more closely.
Domain- The set of input values of a relation.
Range- The input values of a relation.
Asymptote- A line that a graph approaches more and more closely.
Essential Information
A rational function has the form f(x)= p(x)/q(x) where p(x) and q(x) are polynomials and q(x)≠0. The inverse variation function f(x)=a/x is a rational function.
Parent Function for Simple Rational Functions The graph of the parent function f(x)= 1/x, is a hyperbola, which consists of two symmetrical parts called branches. The domain and range are all nonzero real numbers. Any function of the form g(x)=a/x (a≠0) has the same asymptotes, domain, and range as the function f(x)= 1/x. |
Graphing Translations of Simple Rational Functions
Graph rational functions in the form y=a/(x-h) +k
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Other Rational Functions
All rational function of the form y=(ax + b)/(cx + d) also have graphs that are hyperbolas.
All rational function of the form y=(ax + b)/(cx + d) also have graphs that are hyperbolas.
- The vertical asymptote of the graph is the line x= -d/c, because the function is undefined when the denominator cx+d is zero.
- The horizontal asymptote is the line y=a/c.