IM Alg2.2.19 Lesson: End Behavior of Rational Functions
Complete all three representations of the polynomial division following the forms of the integer division.
In 2000, the Environmental Protection Agency (EPA) reported a combined fuel efficiency for cars that assumes 55% city driving and 45% highway driving. The expression for the combined fuel efficiency of a car that gets mpg in the city and mpg on the highway can be written as . Several conventional cars have a fuel economy for highway driving is that is about 10 mpg higher than for city driving. That is, . Write a function that represents the combined fuel efficiency for cars like these in terms of .
Rewrite in the form where and are polynomials.
Complete the table to explore the end behavior for rational functions.
What do you notice about the end behavior of different types of rational functions?
Graph y=j(x) and the line it approaches.
Under what conditions would the end behavior of the graph of a rational function approach a line that is not horizontal?
Create a rational function that approaches the line as gets larger and larger in either the positive or negative direction.