When a graph is translated to the right by a units, the x-coordinate of each point on the graph increases by a units. So the equation of the transformed function will have x - a in it.
When a graph is translated down by b units, the y-coordinate of each point on the graph decreases by b units. So the equation of the transformed function will have y - b in it.
Given f(x) = |x| + 5 and the graph of f(x) is transformed into the graph of g(x) by a translation of 4 units right and a translation of 3 units down, the equation of the transformed function g(x) will be:
g(x) = f(x - 4) - 3
This is because the x-coordinate increases by 4 units and the y-coordinate decreases by 3 units.
So the equation of g(x) is:
g(x) = |x-4| + 5 - 3
g(x) = |x-4| + 2
This function g(x) will have the same shape as f(x) but shifted 4 units to the right and 3 units down.