Given: A function G(x)
[tex]G(x)=\frac{1}{x}[/tex]Required: To shift the given function 4 units to the left and 4 units up.
Explanation: To shift a function G(x), 4 units to the left we add 4 in the function's paranthesis-
[tex]G(x)=\frac{1}{x+4}[/tex]Now to shift this function 4 units up we add 4 outside the function i.e.,
[tex]G(x)=\frac{1}{x+4}+4[/tex]Final Answer: After shifting the new function is-
[tex]G(x)=\frac{1}{x+4}+4[/tex]