# 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.

- 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.