[size=150]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 [math]x[/math] mpg in the city and [math]h[/math] mpg on the highway can be written as [math]\frac{100xh}{55x+45h}[/math].[/size][br][br]Several conventional cars have a fuel economy for highway driving is that is about 10 mpg higher than for city driving. That is, [math]h=x+10[/math]. Write a function [math]f[/math] that represents the combined fuel efficiency for cars like these in terms of [math]x[/math].[br]

Rewrite [math]f[/math] in the form [math]q(x)+\frac{r(x)}{b(x)}[/math] where [math]q(x),r(x),[/math] and [math]b(x)[/math] are polynomials.[br]

What do you notice about the end behavior of different types of rational functions?[br]

Under what conditions would the end behavior of the graph of a rational function approach a line that is not horizontal?[br]

Create a rational function that approaches the line [math]y=2x-3[/math] as [math]x[/math] gets larger and larger in either the positive or negative direction.