Question 85096
The answer to this problem will probably be easier to understand if you can see what the
two given graphs look like. So let's begin by graphing {{{y = abs(x)}}} and {{{y = abs(x+4)-3}}}:
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{{{graph(300,300,-10,10,-5,10,abs(x),abs(x+4)-3)}}}
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The brown graph is the graph of {{{y = abs(x)}}} and the green graph is is the graph of
{{{y = abs(x+4)-3}}}
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Notice that if you take the graph of {{{y = abs(x)}}} and move it 4 units to the left and
then down 3 units, you get the graph of {{{y = abs(x+4)-3}}}. The 4 units to the left comes
from the x+4 in the absolute value signs. The sign of the 4 is + so you move in the opposite
direction, that is move in the minus direction 4 units.  When you do that you get the graph of
{{{y = abs(x+4)}}} which is shown in purple on the graph below:
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{{{graph(300,300,-10,10,-5,10,abs(x),abs(x+4)-3,abs(x+4))}}}
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Then the -3 of the original translation comes into play. It lowers the purple graph by
3 units so that it sits on top of the green graph.
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In summary, take the original graph of {{{y = abs(x)}}} and shift it to the left 4 units, and
then shift it down 3 units to get the graph of {{{y = abs(x+4)-3}}}
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Hope this helps you to visualize what is happening with the translation.