Being Respectful of Rational Functions
IN THIS CHAPTER
Investigating domains and related vertical asymptotes
Looking at limits and horizontal asymptotes
Removing discontinuities of rational functions
The best way to investigate rational functions is to look at the intercepts, the asymptotes, any removable discontinuities, and the limits to tell where the function values have been, what they’re doing for particular values of the domain, and what they’ll be doing for large values of x. You also need all this information to discuss or graph a rational function.
Whether you’re graphing rational functions by hand or with a graphing calculator, you need to be able to recognize the various characteristics (intercepts, asymptotes, and so on) of the rational function. And, if you don’t know what these characteristics are and how to find them, your calculator is no better than a paperweight to you.
Examining Rational Functions
You see rational functions written, in general, in the form of a fraction:
, where f and g are polynomials
Rational functions (and more specifically their ...