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Given the base function y=|x|, y=|x-h|+k will be translated h units left/right (right if h>0, left if h<0) and k units up/down (up if k>0, down if k<0).
So the graph of y=|x+3|-2 will be the graph of y=|x| shifted 3 units left (Note that h=-3; x-(-3)=x+3) and 2 units down. The vertex will be at (-3,-2), the graph opens up, and the sides have slope of `+-1` .
The graph of y=|x| in black and y=|x+3|-2 in red:
Note that a graph of a function with absolute value is V-shaped.
To determine the graph of it, consider the graph of function y=|x| which is :
Then, apply the transformation of axis. So isolate the expression of with absolute value in the given equation. To do so, add both sides by 2.
`y = |x+3|-2`
Now, consider each side of the equation.
For y+c, it means that the original graph is shifted c units down. So, move the graph of `y=|x|` two (2) units down.
And for x + c, it means that the original graph is shifted c units to the left. So, move the graph of `y=|x|` three (3) units to the left.
Hence, the graph of `y=|x+3|-2` is:
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