Rational Functions

Question

How are rational functions similar to linear, quadratic, or exponential functions? How are they different? When are these similarities or differences important when looking for intersections between rational functions and other types of functions? 

Answer 1

I think Kevin's comment above is very good.

I would add the following.

Linear, quadratic...and in fact, polynomial functions of all degrees are continuous and differentiable on the the whole real line. So is the exponential function (which is in some ways not surprising considering the ability to express the exponential function as an infinite series). Also on any closed interval these functions are bounded.

The rational functions, however, are NOT continuous and NOT bounded. Rational functions are discontinuous and unbounded at zeros of the denominator.