Given:
The parent function |x| is a modulus function.
The mod function is defined as:
[tex]|x|=\begin{cases}x,x\ge0 \\ -x,x<0\end{cases}[/tex]
The points on the graph for this function will be (0,0) , (1,1), (-1,1),...etc
Hence, the graph will be drawn as:
Now, the graph of g(x) = |x+3|-4 is drawn by shifting graph of |x| 3 units to the left and 4 units down.
The graph is shown below,
Now, to obtain the graph g(x) that is shifted 5 units left and 2 units up is given by the equation:
[tex]g(x)=|x+5|+2[/tex]
