To determine the new equation when the function \( G(x) = \frac{1}{x} \) is shifted 4 units to the left and 4 units up, follow these steps:
1. Horizontal Shift: A shift to the left by 4 units means replacing \( x \) with \( x + 4 \) in the function. This horizontal shift modifies the original function \( G(x) = \frac{1}{x} \) to become \( G(x) = \frac{1}{x+4} \).
2. Vertical Shift: A shift upward by 4 units means adding 4 to the entire function. Thus, the function \( G(x) = \frac{1}{x+4} \) becomes \( G(x) = \frac{1}{x+4} + 4 \).
So, combining these transformations, the new function is:
[tex]\[ G(x) = \frac{1}{x+4} + 4 \][/tex]
Therefore, the correct choice is:
B. [tex]\( G(x) = \frac{1}{(x+4)} + 4 \)[/tex]
