Precalculus Exponential and Logarithmic Functions Graphs of Functions
Graph of the Logarithmic Function
   Interactive Example 1

Definition 1
.
For a > 0 and a is not equal to 1,
y = logax   means   ay = x.

Definition 2
.
If a > 0 and a is not equal to 1, then the logarithmic function of base a is defined to be
f(x) = logax .

Graph of f(x) = log a x , 0 < a < 1 Graph of f(x) = log a x , a > 1
 
 
a =    
a =    

Statement 
.
PROPERTIES OF THE LOGARITHMIC FUNCTION

The domain of f is the set of positive real numbers.
The range of f is the set of all real numbers.
The x-intercept for the graph of f is 1. The graph of f has no y-intercept.
The y-axis is a vertical asymptote for the graph of f.
The function f is increasing if a > 1 and decreasing if 0 < a < 1.
The function f is one - to - one.


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