4.6 Transformations of Exponential Functions.notebook
4.6 Transformations of Exponential Functions.notebook May 12, 2015 4.6 Transformations of Exponential Functions 2015 05 12 Today we will review the concept of transformations and examine how each transformation affects the graphs of exponential functions. All exponential functions can be written in the form where 'b' is the base of the exponential equation. 1 4.6 Transformations of Exponential Functions.notebook May 12, 2015 The transformations of this function are the same as with each of the other functions we have examined throughout this course. 'a' When a < 0 ‐reflection in the x‐axis. When a > 1 ‐ vertical stretch by a factor of a. When 0 < a < 1‐ vertical compression by a factor of a. 'k' When k < 0 ‐ reflection in the y‐axis When k > 1 ‐ horizontal compression by a factor of 1 / k When 0 < k < 1 ‐horizontal stretch by 1 / k 'd' When d > 0 ‐horizontal translation d units right When d < 0 ‐horizontal translation d units left 'c' When c > 0 ‐vertical translation c units up When c < 0 ‐vertical translation c units down 2 4.6 Transformations of Exponential Functions.notebook May 12, 2015 Ex. Determine the base function of each of the following exponential functions, then determine transformations to each function. 3 4.6 Transformations of Exponential Functions.notebook May 12, 2015 4 4.6 Transformations of Exponential Functions.notebook May 12, 2015 Ex. Determine the equation of an exponential function that has the following properties: ‐ a base of 3 ‐ vertically stretched by a factor of 2 ‐ vertically translated 3 units up ‐ a reflection in the x‐axis 5 4.6 Transformations of Exponential Functions.notebook May 12, 2015 Graphing Each Individual Transformation Graph each individual transformation one at a time in the order a, k, d, c. Ex. Identify the transformations of the following function, then graph the function by applying each transformation in order 6 4.6 Transformations of Exponential Functions.notebook May 12, 2015 Pg. 251 #2‐4,7‐9,11,12 tomorrow 4.7 Thursday Ch.4 Review Next Wednesday Ch. 4 Test 7
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