Question

understanding translations of the parent function
consider the following function: $y = \frac{1}{(x + 5)} + 2$
how does the graph of this function compare with the graph of the parent function, $y = \frac{1}{x}$?
\\(\circ\\) it is shifted right 5 units and up 2 units from the parent function.
\\(\circ\\) it is shifted left 5 units and up 2 units from the parent function.
\\(\circ\\) it is shifted right 5 units and down 2 units from the parent function.
\\(\circ\\) it is shifted left 2 units and down 5 units from the parent function.
\\(\circ\\) it is shifted right 2 units and up 5 units from the parent function.
\\(\circ\\) it is shifted left 2 units and up 5 units from the parent function.
done

Explanation:

For rational parent function $y=\frac{1}{x}$, horizontal shifts follow $y=\frac{1}{x-h}$ (right $h$ units if $h>0$, left $|h|$ units if $h<0$) and vertical shifts follow $y=\frac{1}{x}+k$ (up $k$ units if $k>0$). For $y=\frac{1}{x+5}+2$, rewrite as $y=\frac{1}{x-(-5)}+2$: $h=-5$ means left 5 units, $k=2$ means up 2 units.

Answer:

It is shifted left 5 units and up 2 units from the parent function.