f(x)=(1)/(x-9)+2 Describe the transformations from the parent function, f(x)=1/x Shift right 9 units shift down 2 units Shift right 2 units shift down 9 units Shift left 9 units, shift up 2 units Shift right 9 units shift up 2 units

To describe the transformations from the parent function $f(x)=\frac{1}{x}$ to the given function $f(x)=\frac{1}{x-9}+2$, we need to analyze the changes in the function.<br /><br />The given function can be written as $f(x)=\frac{1}{x-9}+2$.<br /><br />Comparing this with the parent function $f(x)=\frac{1}{x}$, we can see that there are two transformations:<br /><br />1. Horizontal shift: The term $(x-9)$ in the denominator indicates a horizontal shift of 9 units to the right. This means that the graph of the parent function $f(x)=\frac{1}{x}$ is shifted 9 units to the right to obtain the graph of the given function $f(x)=\frac{1}{x-9}$.<br /><br />2. Vertical shift: The term $+2$ in the given function indicates a vertical shift of 2 units upward. This means that the graph of the function $f(x)=\frac{1}{x-9}$ is shifted 2 units upward to obtain the graph of the given function $f(x)=\frac{1}{x-9}+2$.<br /><br />Therefore, the correct description of the transformations from the parent function $f(x)=\frac{1}{x}$ to the given function $f(x)=\frac{1}{x-9}+2$ is:<br /><br />Shift right 9 units, shift up 2 units.