Step-by-step explanation:
recall for any function f(x)
Vertical translations by "a" units are given simply by
f(x) + a,
where positive values of a translates the graph in the positive y direction (i.e up) and negative values of a translates the graph in the negative y direction (i.e down)
Horizontal translations by "b" units are given by
f(x-b),
where negative values of a translates the graph in the negative x direction (i.e left) and postive values of a translates the graph in the postive x direction (i.e right)
if we combine the two above, we get the expression
g(x) = f(x-b) + a
In our case, we see that to get from the blue graph to the red graph, we need to translate 3 units in the positive x-direction (i.e b = 3) and 4 units in the negative y-direction (i.e a = -4)
Substituting b = 3, a = -4 and that f(x) = |x|,
we get
g(x) = |x-(3)| - 4
g(x) = |(x-3)| - 4
