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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 ______________________.
Do better in math today
1.
Functions
1.1
Function notation
1.2
Identifying functions
1.3
Adding functions
1.4
Subtracting functions
1.5
Multiplying functions
1.6
Dividing functions
1.7
Composite functions
1.8
Reflection across the y-axis: y=f(−x)
1.9
Reflection across the x-axis: y=−f(x)
1.10
Transformations of functions: Horizontal translations
1.11
Transformations of functions: Vertical translations
1.12
Transformations of functions: Horizontal stretches
1.13
Transformations of functions: Vertical stretches
1.14
Introduction to linear equations
1.15
Even and odd functions
1.16
One to one functions
1.17
Difference quotient: applications of functions