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)
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)=x2 or f(x)=x3.
More pages and topics related to graph transformation (scaling, shifting) can be found in this site.