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# Class Note for MATH 1310 at UH 2

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This 9 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 20 views.

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Date Created: 02/06/15

Math 13 10 Chapter 5 Section 51 Exponential Functions Exponential Function With base b For I gt 0 a function f of the form fX bx is called the exponential function With base b Characteristics of Exponential Functions of the form fxbx The graphs of all exponential functions of the form f x bx 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 00 If I gt 1 then the graph of f x bx looks like If 0 lt b lt 1 then the graph of f x bx looks like y Example 1 Graph the following pair of functions on the same set of axes fx 22 gm 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 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 2 1 1 Example 3 Apply transformations to sketch the graph of the following function Show the asymptote and then state the domain and range of the function fx 1 Example 4 Apply transformations to sketch the graph of the following function Show the asymptote and then state the domain and range of the function W 4r 1 Example 5 Find the exponential function of the form f x axthat passes through 0 l and 4 16

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