3: Rational Functions
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”In everything one thing is impossible: rationality.” - Friedrich Nietzsche
Chapter three attempts to tackle the slightly sticky interaction between limits and division. Since division by zero is a generally frowned upon mathematical operation, we run into a few new wrinkles that limits can help us to understand better.
We begin with the limit law for division of two functions, which immediately inspires the fraction version of polynomials: rational functions. We explore how to add, subtract, multiply, divide, and find domains of these functions. This allows us to also solve equations and inequalities involving rational functions
Limits of rational functions can be quite easy as long as we avoid division by zero. In the situations where the limit brings a denominator to zero, we discuss different methods to decipher the limit value.
These limits tell us about the shape of the graph for a given rational function (which will be useful later), but also help us better define when a given function has vertical or horizontal asymptote(s).
Click through the following links to read this chapter.