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.
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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
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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.
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4.6 Transformations of Exponential Functions.notebook
May 12, 2015
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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
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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
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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
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