To compare the graph of
to the graph of
we need to consider how the transformation g(x) affects the original function f(x).
The transformation g(x) can be broken down into two parts: the addition of 4 inside the cube root function and the subtraction of 3 outside the cube root function. Adding 4 inside the cube root function,
shifts the graph of f(x) to the left by 4 units. This means that every point on the graph of g(x) is 4 units to the left compared to the corresponding point on the graph of f(x).
Subtracting 3 outside the cube root function,
shifts the graph of g(x) downward by 3 units. This means that every point on the graph of g(x) is 3 units below the corresponding point on the graph of f(x).
Overall, the graph of
is a shifted and downward shifted version of the graph of