Question

The graph of g(x) is transformed from its parent function, f(x). Apply concepts involved in determining the key features of a rational function to determine the domain and range of the function, g(x)=1/x+4 . A. What is the domain of the function, g(x)? B. What is the range of the function, g(x)?

Answer 1

Presumably, the parent function is
f(x) = 1/x
Then g(x) = f(x +4) represents a translation of the function 4 units to the left.

The domain and range of f(x) are "all real numbers except x=0".

A. The domain of g(x) will have that exception translated 4 units to the left, to x = -4. The domain of g(x) is ...
all real numbers except x = -4.

B. The range of g(x) remains unchanged from that of f(x). It is ...
all real numbers except g(x) = 0.