Precalculus 3.1-3.3 Test Outline

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3.1 Exponential functions and their graphs

  • graphs
    • transformations of exponentials
    • domain, range, intercept, asymptote
  • natural base
  • calculating interest (formulas are provided)
  • growth and decay (formulas provided)

3.2 Logarithmic functions and their graphs

  • common log (log base 10) and natural log (log base e, ln)
  • logarithms ask a question: logbasex means what power of the base is x?
  • logarithms are inverses of exponentials of the same base
  • rewrite logarithms as exponentials
  • properties
    • logb1 = 0
    • logbb = 1
    • logbbx = x and blogbx = x (inverses!)
    • if logbx = logby, then x = y
  • graphs
    • transformations of logarithms
    • domain, range, intercept, asymptote

3.3 Properties of Logarithms

  • change of base formula
  • properties
    • product
    • quotient
    • power
  • expanding
  • condensing
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