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Transformations of functions: Horizontal translations
- Lesson: 144:31
- Lesson: 212:09
Transformations of functions: Horizontal translations
Horizontal translations refer to movements of a graph of a function horizontally along the x-axis by changing the x values. So, if y = f(x), then y = (x –h) results in a horizontal shift. If h > 0, then the graph shifts h units to the right; while If h < 0, then the graph shifts h units to the right.
Basic concepts: Completing the square, Converting from general to vertex form by completing the square, Shortcut: Vertex formula,
Related concepts: Graphing transformations of trigonometric functions, Determining trigonometric functions given their graphs,
Lessons
Compared to y=f(x):
y=f(x−8): shift 8 units to the right
y=f(x+3): shift 3 units to the left
y=f(x−8): shift 8 units to the right
y=f(x+3): shift 3 units to the left
- 1.a)Sketch the following functions on the same set of coordinate axes:
y=(x)2 VS. y=(x−6)2 VS. y=(x+5)2b)Compared to the graph of y=x2:
• the graph of y=(x−6)2 is translated "horizontally" ________ units to the ______________.
• the graph of y=(x+5)2 is translated "horizontally" ________ units to the ______________. - 2.Horizontal Translations
Given the graph of y=f(x) as shown, sketch:a)y=f(x−8)b)y=f(x+3)c)In conclusion:
• (x)→(x−8): shift __________ to the __________. All x coordinates ⇒ ____________________
• (x)→(x+3): shift __________ to the __________. All x coordinates ⇒ ____________________
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3.
Transformations of Functions
3.1
Transformations of functions: Horizontal translations
3.2
Transformations of functions: Vertical translations
3.3
Reflection across the y-axis: y=f(−x)
3.4
Reflection across the x-axis: y=−f(x)
3.5
Transformations of functions: Horizontal stretches
3.6
Transformations of functions: Vertical stretches
3.7
Combining transformations of functions
3.8
Even and odd functions
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Transformations of functions: Horizontal translations
Don't just watch, practice makes perfect.
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