Precalculus A Fuctional Approach to Graphing and Problem Solving
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Section 4.1: Rational Functions
Essential Ideas
  • A rational function f is the quotient of polynomial functions defined by
    P(x) and D(x) so that
                          f (x) = P(x)/D(x)   where D(x) does not equal 0

  • Discontinuities of rational functions are either deleted points or vertical asymptotes.

  • Asymptotes
    Let f (x) = P(x)/D(x) where P   is a polynomial function with leading coefficient P and D is a polynomial function with leading coefficient d. Moreover, P(x) and D(x) and have no common factors
    Vertical
    The vertical asymptote is the line x = c where D(c) = 0. That is, values that cause division by 0.
    Horizontal
    If P(x) has degree m and D(x) has degree n , then the horizontal asymptote is y = 0 if m < n and it is the horizontal line y = P /d
    if m = n.
    Oblique
    If the degree of P is one more than the degree of D, then carry out the division to find the oblique asymptote y = mx + b.
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© 2011 Karl J. Smith. All rights reserved.