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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 _____________________________.
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2.
Transformations
2.1
Transformations of functions: Horizontal translations
2.2
Transformations of functions: Vertical translations
2.3
Reflection across the y-axis: y=f(−x)
2.4
Reflection across the x-axis: y=−f(x)
2.5
Transformations of functions: Horizontal stretches
2.6
Transformations of functions: Vertical stretches
2.7
Combining transformations of functions
2.8
Even and odd functions