Chapter 8.1-8.3 Test Outline
From Huben's Wiki
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.
- 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.