Transformations of functions: Horizontal translations
Examples
Lessons
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- Sketch the following functions on the same set of coordinate axes:
y=(x)2 VS. y=(x−6)2 VS. y=(x+5)2 - 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 ______________.
- Sketch the following functions on the same set of coordinate axes:
- Horizontal Translations
Given the graph of y=f(x) as shown, sketch:- y=f(x−8)
- y=f(x+3)
- In conclusion:
• (x)→(x−8): shift __________ to the __________. All x coordinates ⇒ ____________________
• (x)→(x+3): shift __________ to the __________. All x coordinates ⇒ ____________________
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Topic Notes
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 left.
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
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