Exponential & Logarithmic Functions (DP IB Analysis & Approaches (AA)): Revision Note

An exponential function is defined by 

Its domain is the set of all real values

Its range is the set of all positive real values

An important exponential function is 

• Where e is the mathematical constant 2.718…

Any exponential function can be written using e

• 

  • This is given in the formula booklet

The graphs have a y-intercept at (0, 1)

The graph will always pass through the point (1, a)

The graphs do not have any roots

The graphs have a horizontal asymptote at the x-axis: 

• For a > 1 this is the limiting value when x tends to negative infinity

• For 0 < a < 1 this is the limiting value when x tends to positive infinity

The graphs do not have any minimum or maximum points

A logarithmic function is of the form 

Its domain is the set of all positive real values

• You can't take a log of zero or a negative number

Its range is set of all real values

and  are inverse functions

An important logarithmic function is 

• This is the natural logarithmic function 

• This is the inverse of 

  • and 

Any logarithmic function can be written using ln

• using the change of base formula

The graphs do not have a y-intercept

The graphs have one root at (1, 0)

The graphs will always pass through the point (a, 1)

The graphs have a vertical asymptote at the y-axis: 

The graphs do not have any minimum or maximum points