Precalculus 3.1-3.3 Test Outline

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: log_basex means what power of the base is x?
• logarithms are inverses of exponentials of the same base
• rewrite logarithms as exponentials
• properties
  • log_b1 = 0
  • log_bb = 1
  • log_bb^x = x and b^log_bx = x (inverses!)
  • if log_bx = log_by, 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