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Transformations of functions: Vertical translations
- Intro Lesson12:33
- Lesson: 112:33
Transformations of functions: Vertical translations
Vertical translations refer to movements of a graph of a function vertically along the y-axis by changing the y values. So, if y = f(x), then y = (x) + h results in a vertical shift. If h > 0, then the graph shifts h units up; while If h < 0, then the graph shifts h units down.
Basic Concepts: Completing the square, Converting from general to vertex form by completing the square, Shortcut: Vertex formula, Graphing parabolas for given quadratic functions
Related Concepts: Graphing transformations of trigonometric functions, Determining trigonometric functions given their graphs
Lessons
- IntroductionAn Experiment to Study "Vertical Translations"
Sketch and compare: (y)=x2 VS. (y−3)=x2 VS. (y+2)=x2a)Sketch all three quadratic functions on the same set of coordinate axes.b)Compared to the graph of y=x2:
• the graph of (y−3)=x2 is translated "vertically" ________ units _____________.
• the graph of (y+2)=x2 is translated "vertically" ________ units _____________. - 1.Vertical Translations
Given the graph of y=f(x) as shown, sketch:a)y=f(x)−8b)y=f(x)+3c)In conclusion:
• (y)→(y+8): shift ________ units ______________ ⇒ all y coordinates _____________________________.
• (y)→(y−3): shift ________ units ______________ ⇒ all y 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