Objectives: Evaluate Exponential Functions Graph Exponential Functions Define the Number e.

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Presentation transcript:

Objectives: Evaluate Exponential Functions Graph Exponential Functions Define the Number e

 The exponential function with base is defined by where is a positive constant other than 1 and is any real number.  Domain:  THM: For an exponential function, if x is any real number then

 1.The domain of consists of all real numbers. The range of consists of all positive real numbers  2.The graphs of all exponential functions of the form pass through the point because. The y-intercept is 1.  3.If, has a graph that goes up to the right and is an increasing function. The greater the value of, the steeper the increase  4.If, has a graph that goes down to the right and is a decreasing function. The smaller the value of, the steeper the decrease.  5. is a one-to-one function.  6.The graph of approaches, but does not touch, the x-axis. The x-axis is a horizontal asymptote. There are no x-intercepts.  7.The graphs of all exponential functions of the form pass through the points are smooth and continuous.

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