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# Class Note for MATH 1310 at UH

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COURSE
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This 6 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 21 views.

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Date Created: 02/06/15
Math 13 10 Chapter 5 Section 52 The Number 6 Natural Exponential Function The exponential function With base e f x 2 ex is called the natural exponential function The number e is an irrational number and is defined as the value that 11 approaches as n n becomes large To five decimal places 6 H 271828 Characteristics of the Natural Exponential Function 0 The graph pass through the key point 0 l o The xaxis y 0 is the horizontal asymptote The domain is all real numbers and the range is 0 oo The graph 0ffx 2 ex looks like Transformations of Functions Horizontal Shifts To graph the function y x 7 c c gt 0 shift the graph of y x to the right 0 units To graph the function y x c c gt 0 shift the graph of y x to the left 0 units Vertical Shifts To graph the function y x c c gt 0 shift the graph of y x upward 0 units To graph the function y x c c gt 0 shift the graph of y x downward 0 units Re ection about the xaXis To graph the function y x re ect the graph of y x in the xaXis Note The sign of the y values will change Re ection about the yaXis To graph the function y x re ect the graph of y x in the yaXis Note The sign of the x values will change Vertical Stretching To graph the function y a x a gt I stretch the graph of y x vertically by a factor of a Vertical Shrinking To graph the function y a x 0 lt a lt l shrink the graph of y x vertically by a factor of a Recommended Order for Transformations of Functions 1 Vertical Stretching or Vertical Shrinking 2 Re ection in the xaXis 3 Horizontal and Vertical Translations 4 Re ection in the yaXis Example 1 Apply transformations to sketch the graph of the following function Show the asymptote and then state the domain and range of the function fx 6H 2 Example 2 Apply transformations to sketch the graph of the following function Show the asymptote and then state the domain and range of the function fx e x 1 l

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