SOLUTION: I have a question that states: use the graph of f(x)=/x/ to find the graph of f(x)=/x+4/-3.

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Question 85096: I have a question that states: use the graph of f(x)=/x/ to find the graph of f(x)=/x+4/-3.
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
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%28x%29 and y+=+abs%28x%2B4%29-3:
.
graph%28300%2C300%2C-10%2C10%2C-5%2C10%2Cabs%28x%29%2Cabs%28x%2B4%29-3%29
.
The brown graph is the graph of y+=+abs%28x%29 and the green graph is is the graph of
y+=+abs%28x%2B4%29-3
.
Notice that if you take the graph of y+=+abs%28x%29 and move it 4 units to the left and
then down 3 units, you get the graph of y+=+abs%28x%2B4%29-3. 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%28x%2B4%29 which is shown in purple on the graph below:
.
graph%28300%2C300%2C-10%2C10%2C-5%2C10%2Cabs%28x%29%2Cabs%28x%2B4%29-3%2Cabs%28x%2B4%29%29
.
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.
.
In summary, take the original graph of y+=+abs%28x%29 and shift it to the left 4 units, and
then shift it down 3 units to get the graph of y+=+abs%28x%2B4%29-3
.
Hope this helps you to visualize what is happening with the translation.