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Vertical Shifting or translation of Graphs

This applet allows you to explore interactively the vertical shifting or translation of the graph of a function.

A constant d is added to a function f(x) and its graph is investigated by changing d. The function to be analyzed is of the form

g(x) = f(x) + d

where f(x) is any of the functions:

f(x)=||x| - 2| ( a "W" shaped graph)

f(x)=x
2 or

f(x)=x
3.

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TUTORIAL How does the addition of a constant to a function affect the graph of this function ?

1-use the scroll bar to set the constant to different values and observe the effect on the graph.

What is the range of values of the constant that create a vertical shifting
up ?

What is the range of values of the constant that create a vertical shifting
down? Explain analytically.

NOTE: You have the choice (left panel, top) of any of the three functions f(x)=||x|-2| (this has a "W" shaped graph), f(x)=x
2 or f(x)=x3.

More pages and topics related to graph transformation (scaling, shifting) can be found in this site.



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