Chapter 8.1-8.3 Test Outline

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8.1 Multiplying and dividing Rational Expressions

  • SImplifying by cancelling common factors.
    • Factor numerators and denominators.
    • The factor of -1 trick.
  • When are rational expressions undefined?
    • Implicit: when the denominator is 0 because a factor is 0.
    • Explicit: when you are told so.
  • Multiplying: multiply the two numerators and multiply the two denominators.
  • Dividing: multiply by the reciprocal of the divisor.
  • Complex fractions: really just a division.

8.2 Adding and Subtracting Rational Expressions

  • Find LCM's (Least Common Mutipliers) of polynomials.
    • Factor each polynomial
    • Choose the biggest power of each factor.
  • Add and subtract rational expressions.
    • Find LCD (Least Common Denominator = LCM denominators.)
    • Multiply numerators and denominators to put them over LCD.
    • Combine and simplify.
  • Use these techniques for straightforward problems.

8.3 Graphing Rational Functions

  • Continuity, vertical asymptote, point discontinuity (hole)
    • asymptotes are lines that are approached but never touched.
    • Domain excludes vertical asymptotes and holes.
    • Calculators do not graph asymptotes or holes correctly.
  • Find discontinuities when factors in denominator are 0.
    • When simplifying, vertical asymptotes remain and holes disappear.
  • Graphing:
    • Calculators show shape.
    • Use tables to confirm discontinuities, and show horizontal asymptotes.
    • Horizontal asymptotes show at large + or - values of X.
    • Graphs show va, ha, axes, holes.
    • Asymptotes should be written as equations of lines.
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