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Transformations of functions: Vertical stretches
- Intro Lesson23:45
- Lesson: 123:45
Transformations of functions: Vertical stretches
Basic Concepts: Converting from general to vertex form by completing the square, Shortcut: Vertex formula, Transformations of functions: Vertical translations
Related Concepts: Graphing transformations of trigonometric functions, Determining trigonometric functions given their graphs, What is a polynomial function?
Lessons
- IntroductionAn Experiment to Study "Vertical Stretches"
Sketch and compare: (y)=x2+2 VS. (2y)=x2+2 VS. (3y)=x2+2a)a) Sketch all three quadratic functions on the same set of coordinate axes.a)Compared to the graph of (y)=x2+2:
• (2y)=x2+2 is a vertical stretch about the x-axis by a factor of ____________.
• (3y)=x2+2 is a vertical stretch about the x-axis by a factor of ____________. - 1.Vertical Stretches
Given the graph of y=f(x) as shown, sketch:a)y=21f(x)b)y=34f(x)c)In conclusion:
• (y)→(2y): vertical stretch by a factor of ________ ⇒ all y coordinates ______________________.
• (y)→(43y): vertical stretch by a factor of ________ ⇒ all y coordinates ______________________.
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25.
Transformations
25.1
Transformations of functions: Horizontal translations
25.2
Transformations of functions: Vertical translations
25.3
Reflection across the y-axis: y=f(−x)
25.4
Reflection across the x-axis: y=−f(x)
25.5
Transformations of functions: Horizontal stretches
25.6
Transformations of functions: Vertical stretches
25.7
Combining transformations of functions
25.8
Even and odd functions