Investigating logarithmic graphs

Learning objectives:

  • Identify the general formula for a logarithm function 
  • Identify the shape of a logarithmic function
  • Investigate the key characteristics of a logarithmic graph

Task 1: investigating the base 
  1. increase and decrease 'a', describe what you see when a>0
  2. describe what you see when a<0
  3. can a=0?
  4. describe the graph when a=1
  5. what conclusion can you make about the base of a logarithmic graph and how it affects the graph?

Task 2: investigating the asymptote 
  1. describe the graph as you increase and decrease 'b'
  2. describe the graph as you increase and decrease 'A'
  3. describe the graph as you increase and decrease 'h'
  4. describe the graph as you increase and decrease 'k'
  5. Reflection: why do you think the parenthesis A(x-h) was necessary to express the value of the vertical asymptote?


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