MAT150 College Algebra Sections 9'4

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MAT150College AlgebraSections 9.4
9.5Rational Functions
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Rational Functions

• If r can be written as the ratio of polynomial
  functions p(x) and q(x), then r is called a
  rational function
• Standard Form r(x)
• Examples
• Pg413, 1 5

anxn an-1xn-1 a1x ao bmxm bm-1xm-1
b1x bo
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Long-Run Behavior
LONG-RUN BEHAVIOR
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Long-Run Behavior
LONG-RUN BEHAVIOR
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Long-Run Behavior
The long-run behavior of a polynomial function is
determined by its leading term. The long-run
behavior of a rational function, is determined
by the leading terms of p and q
anxn an-1xn-1 a1x ao bmxm bm-1xm-1
b1x bo
anxn bmxm

• r(x)

as x ?8
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Short-Run Behavior

• Using complete the following table
• What is happening as x approaches 2?
• This creates what is called a vertical asymptote
  in the graph

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• Lets revisit the functions we saw earlier
• Determine the vertical asymptotes
• What are the x- and y-intercepts??
• Textbook problem 17 on page 421

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• Determine all intercepts and asymptotes of the
  following functions. Verify by looking at the
  graphs.
• A hole occurs whenever the numerator and the
  denominator have a common factor of the same
  multiplicity

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• Find a Possible Formula
• The graph of f(x) has vertical asymptotes at x-2
  and x1, and a horizontal asymptote at y0. Its
  x-intercept is (3,0).
• The graph of f(x) has vertical asymptotes at x-2
  and x1, and a horizontal asymptote at y4. Its
  x-intercept is (3,0).
• The graph of f(x) has a vertical asymptote at
  x-2, a hole at x3, and a horizontal asymptote
  at y2. Its x-intercepts are (1,0) and (5, 0).
• Textbook problems, pg 422 36, 38

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Due next time Section 9.4 15, 12,
21 Section 9.5 17odd, 17, 19, 23, 27, 35, 36,
38, 40, 41