rational functions

• rational number: ratio of two integers
• rational expression: ratio of 2 polynomials
• to multiply/divide/simplify:

  1. factor
  2. restrict
  3. reduce
• to add/subtract/solve equations/solve compound fractios:

  1. find LCD
  2. method & solve
  3. restrict, simplify
• to divide: multiply by reciprocal
• simplify radical: multiply numerator and denominator by radical over denominator
• rate: work done/time to do it
• average: sum of values/how many values
• vertical asymptote:

  • restrictions on denominator
  • occurs if the factor in the denominator does not also occur in the numerator
• holes (point discontinuity):

  • restrictions on variable
  • occurs if the factor in the denominator is shared by the numerator
  • substitute value into equation to find the y-vale (0,0)
• horizontal asymptote:

  • degree of numerator < degree of denominator (y=0)
  • degree of numerator > degree of denominator (no asymptote)
  • degree of numerator = degree of denominator (y=leading coeff of num/leading coeff of denom)
• to graph:

  • find points using an x-y table and find both intercepts
  • find asymptotes and point discontinuity