Graph Translation
description
Transcript of Graph Translation
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This is a basic tutorial on how graphs are translated by various terms in the equation
James S Jun 2010
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y = x3 + 3
y = x3
The “+ 3” added to x3 adds 3 to every point on the graph and thus moves the whole graph upward. This is true of any shape graph
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y = x + 3
Graph shape is not important to translation
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y = x2 + 3
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y = ln (x) + 3
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y = (x – 3)3 + 3
y = (x)3
In this equation, there is a horizontal shift due to the – 3 inside the parentheses and a vertical shift due to the + 3 outside the parentheses.
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y = (x - 3)3 + 3
y = x3
The combination of horizontal and vertical is a diagonal shift.
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y = (x – 3)2 + 3
Shape of the curve in not important.
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y = (x – 3)2 – 3
Shifted right and down
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y = (x + 3)2 – 3 Shifted left and
down
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y = ln (x – 3) + 3
Shifted right and up
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In any equation in the form: y = (x ± h)c ± k,the “h” inside the parens will shift the graph horizontally, and the “k” outside the parens will shift the graph vertically.
+ h shifts left, – h shifts right
+ k shifts upward, – k shifts downward
James S Jun 2010