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Transformations of functions: Horizontal stretches
- Intro Lesson25:33
- Lesson: 125:33
Transformations of functions: Horizontal stretches
Basic Concepts: Converting from general to vertex form by completing the square, Shortcut: Vertex formula, Transformations of functions: Horizontal translations
Related Concepts: Graphing transformations of trigonometric functions, Determining trigonometric functions given their graphs, What is a polynomial function?
Lessons
- IntroductionAn Experiment to Study "Horizontal Stretches"
Sketch and compare: y=(x−4)2 VS. y=(2x−4)2 VS. y=(3x−4)2a)Sketch all three quadratic functions on the same set of coordinate axes.b)Compared to the graph of y=(x−4)2:
• y=(2x−4)2 is a horizontal stretch about the y-axis by a factor of _____________.
• y=(3x−4)2 is a horizontal stretch about the y-axis by a factor of _____________. - 1.Horizontal Stretches
Given the graph of y=f(x) as shown, sketch:a)y=f(2x)b)y=f(31x)c)In conclusion:
• (x)→(2x): horizontal stretch by a factor of ________ ⇒ all x coordinates ______________________.
• (x)→(31x): horizontal stretch by a factor of ________ ⇒ all x coordinates ______________________.
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8.
Transformations of Functions
8.1
Transformations of functions: Horizontal translations
8.2
Transformations of functions: Vertical translations
8.3
Reflection across the y-axis: y=f(−x)
8.4
Reflection across the x-axis: y=−f(x)
8.5
Transformations of functions: Horizontal stretches
8.6
Transformations of functions: Vertical stretches
8.7
Combining transformations of functions
8.8
Even and odd functions