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Contents
Translation
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Translation
Translation
along the x-axis
Given
the graph y = f(x), to sketch the graph of
y = f(x + a)
translate
the graph of y = f(x) parallel to the x-axis by factor -a.
This
means adding (-a) to every x-coordinate.
 Example:
Sketch the graph of y = x2 - 6x + 7, and hence
sketch the graph of y = x2 - 4x + 8.
Solution:
Graph
of y = x2 - 6x + 7:
Graph
of y = x2 - 4x + 2:
On
inspection, y can be rewritten as:
y = (x + 1)2 - 6 (x + 1) + 7
= f (x + 1)
-->
Translate parallel to the negative x-axis (to the left) by factor 1.
Translate
along the y-axis
Given
the graph y = f(x), to sketch the graph of
y = f(x) + a
translate
y = f(x) parallel to the y-axis with factor a.
This
means adding a to every y-coordinate.
Example:
Sketch the graph of y = 1/x, and hence
sketch the graph of y = 1/x - 1.
Solution:
Graph
of y = 1/x:
Graph
of y = 1/x - 1
= f(x) - 1
-->
Translate parallel to the y axis by -1 units (ie. shift downwards).
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