2.6.1 Properties of Further Graphs

What are the key features of logarithmic graphs?

• A logarithmic function is of the form 
• Remember the natural logarithmic function 
  • This is the inverse of 
    • and 
  • The graphs do not have a y-intercept
    • The graphs have a vertical asymptote at the y-axis: 
  • The graphs have one root at 
    • This can be found using your GDC
  • The graphs do not have any minimum or maximum points
  • The value of b determines whether the graph is increasing or decreasing
    • If b is positive then the graph is increasing
    • If b is negative then the graph is decreasing

What are the key features of logistic graphs?

• A logistic function is of the form 
• L, C & k are positive constants
• Its domain is the set of all real values
• Its range is the set of real positive values less than L
• The y-intercept is at the point 
• There are no roots
• There is a horizontal asymptote at y = L
• This is called the carrying capacity
• This is the upper limit of the function
• For example: it could represent the limit of a population size
• There is a horizontal asymptote at y = 0
• The graph is always increasing