5.2-3 RationalFunctions - Section 5.2(Sullivan 8th ed...

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Section 5.2 (Sullivan, 8 th ed. MAC1140/MAC1147 5.2: RATIONAL FUNCTIONS A rational function R(x) is a quotient of two polynomials p(x)/q(x). The domain consists of all real numbers except those for which the denominator q = 0. An asymptote is a line to which a certain part of the graph of a function gets closer and closer but never touches. A rational function in lowest terms will have a vertical asymptote at any value of x that would cause the denominator q(x) = 0. Proper rational functions, where the degree of the numerator is less than that of the denominator, will have a horizontal asymptote at y = 0 . If the degree of the numerator is greater than or equal to that of the denominator, the horizontal or oblique asymptote can be found by long division; it will be the quotient without the remainder. The real zeros of a rational function are the values for which the numerator p(x) = 0. Graph using transformations; determine domain, range, asymptotes, and real zeros from the graph: 1.
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