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- Transformations of Functions
Combining transformations of functions
- Lesson: 133:42
- Lesson: 244:26
- Lesson: 3a13:54
- Lesson: 3b23:46
- Lesson: 3c28:26
Combining transformations of functions
Basic Concepts: Transformations of functions: Horizontal translations, Transformations of functions: Vertical translations, Transformations of functions: Horizontal stretches, Transformations of functions: Vertical stretches
Related Concepts: Graphing transformations of trigonometric functions, Determining trigonometric functions given their graphs, What is a polynomial function?
Lessons
- 1.Describe the Combination of Transformations
Compared to y=f(x), describe every step of transformations applied to:
y=−2f[3(x+4)]+5 - 2.Write the Equation of a Transformed Function
Transform the function f(x)=x1 into the function g(x) by:a)stretching horizontally by a factor of 2 about the y-axisb)stretching vertically by a factor of 53 about the x-axisc)vertical translation of 7 units upd)reflection in the y-axise)horizontal translation of 4 units to the leftf)reflection in the x-axis
Write the function for g(x). - 3.Use "Coordinate Mapping Formula" to Graph a Transformed Function
Given the graph of y=f(x) as shown,a)describe every step of transformations applied to: y=41f(3−2x)−1b)Graph the transformed function on the same set of coordinate axes.c)Shortcut: use "Coordinate Mapping Formula" to graph the transformed function.
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13.
Transformations of Functions
13.1
Transformations of functions: Horizontal translations
13.2
Transformations of functions: Vertical translations
13.3
Reflection across the y-axis: y=f(−x)
13.4
Reflection across the x-axis: y=−f(x)
13.5
Transformations of functions: Horizontal stretches
13.6
Transformations of functions: Vertical stretches
13.7
Combining transformations of functions