Unformatted text preview: n Section 1.6, we will produce another polynomial function. If, on the other hand, we
divide two polynomial functions, the result may not be a polynomial. In this chapter we study
rational functions - functions which are ratios of polynomials.
Definition 4.1. A rational function is a function which is the ratio of polynomial functions.
Said diﬀerently, r is a rational function if it is of the form
r(x) = p(x)
q (x) where p and q are polynomial functionsa
a According to this deﬁnition, all polynomial functions are also rational functions. (Take q (x) = 1). As we recall from Section 1.5, we have domain issues anytime the denominator of a fraction is
zero. In the example below, we review this concept as well as some of the arithmetic of rational
Example 4.1.1. Find the domain of the following rational functions. Write them in the form
for polynomial functions p and q and simplify.
1. f (x) = 2x − 1
x+1 2. g (x) = 2 − 3
x+1 3. h(x) = 2x2 − 1 3x − 2
x2 − 1
x −1 4. r(x) = p(x)
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