ANSWER
[tex]C.\text{ }g(x)=\frac{1}{x-2}+7[/tex]
EXPLANATION
The given function is:
[tex]f(x)=\frac{1}{x}[/tex]
When a function is shifted vertically upward, it changes as follows:
[tex]g(x)=f(x)+d[/tex]
where d = number of units that it is shifted
Therefore, shifting f(x) by 7 units up will result in the following function:
[tex]g(x0=\frac{1}{x}+7[/tex]
When a function is shifted horizontally to the right, it changes as follows:
[tex]g(x)=f(x-c)[/tex]
where c = number of units that it is shifted
Hence, transforming the function above by shifting it 2 units to the right will result in:
[tex]g(x)=\frac{1}{x-2}+7[/tex]
The correct answer is option C.
