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

Definition 
.
If a > 0 and a is not equal to 1, the exponential function with base a is defined to be
f(x) = a x .

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

Statement 
.
PROPERTIES OF THE EXPONENTIAL FUNCTION

The domain of f is the set of all real numbers.
The range of f is the set of positive real numbers.
The y-intercept for the graph of f is 1. The graph of f has no x-intercept.
The x-axis is a horizontal 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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