In order to find the equation, let's use the parent function f(x) = |x|, which has the following graph:
Then, looking at the given graph, we can see that the lowest point is at (-3, 4), and the parent function has the lowest point at (0, 0).
So, in order to translate the parent function into the given function, we need a translation of 3 units left and 4 units up.
A translation of 3 units left can be written as an increase in the value of x by 3 units:
[tex]f^{\prime}(x)=|x+3|[/tex]
Then, a translation of 4 units up can be written as an increase in the value of f'(x) by 4 units:
[tex]g(x)=|x+3|+4[/tex]
