Final answer:
The function g(x) = 1/(x+3) — 4 is derived from the parent function f(x) = 1/x by shifting it 3 units to the left and then 4 units down.
Step-by-step explanation:
To describe the transformations of the parent function f(x) = 1/x, into the function g(x) = 1/(x+3) — 4, we look at each modification separately.
Firstly, the term (x+3) in the denominator indicates a horizontal shift. According to our understanding that f(x + d) represents a translation of the function in the negative x-direction by a distance d, the +3 inside the parentheses causes the graph of the parent function to shift 3 units to the left.
Secondly, the subtraction of 4 at the end of the function indicates a vertical shift. The parent function is moved 4 units down.
Overall, the parent function f(x) = 1/x is shifted 3 units to the left and 4 units down to achieve the function g(x) = 1/(x+3) — 4.