Increasing And Decreasing - Exponentials

 

Definition: A function is said to be increasing on the interval (a, b) if whenever x1 and x2 are two numbers in the interval such that x1 < x2 then f(x1) < f(x2).  Another way to look at this is: As you trace the graph from a to b (that is from left to right) the graph should go up.

Definition: A function is said to be decreasing on the interval (a, b) if whenever x1 and x2 are two numbers in the interval such that x1 < x2 then f(x1) > f(x2).  Another way to look at this is: As you trace the graph from a to b (that is from left to right) the graph should go down.

 

Of course, as the functions become more complicated so do determining the intervals over which the function is increasing and decreasing.  In general, to determine the intervals of increasing and decreasing:

 

 

 

 

Practice

As mentioned earlier, determining the intervals of increasing and decreasing of a function often require the use of a graphing utility.  For this reason it is suggested that you use a graphing calculator or some other graphing utility, such as the one provided below.  There are ten problems in the Practice Problems set that you can test your skills with.  The answers are also provided.

Instructions Using Program (Word Document)

 

 

Practice finding range

Practice Problems

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