Step 1
We will start with the graph of the standard/parent function \(\displaystyle{y}={\frac{{{1}}}{{{x}}}}\)
When we reflect the graph of \(\displaystyle{y}={f{{\left({x}\right)}}}\) in the x-axis, we get the graph of \(\displaystyle{y}=-{f{{\left({x}\right)}}}\)
Therefore, the graph of \(\displaystyle{y}=-{\frac{{{1}}}{{{x}}}}\) is obtained by reflecting the graph of PSKy=\frac{1}{x} in the x-axis.
In the graph below:
The blue dashed curve represents \(\displaystyle{y}={\frac{{{1}}}{{{x}}}}\)
The red solid curve represents \(\displaystyle{y}=-{\frac{{{1}}}{{{x}}}}\)
Step 2
When we shift the graph of \(\displaystyle{y}={f{{\left({x}\right)}}}\) by k units in the upward direction, we get the graph of \(\displaystyle{y}={f{{\left({x}\right)}}}+{k}\)
Therefore, the graph of \(\displaystyle{y}={1}-{\frac{{{1}}}{{{x}}}}\) is obtained by shifting the graph of \(\displaystyle{y}=-{\frac{{{1}}}{{{x}}}}\) by 1 unit in the upward direction.
In the graph below:
The red dashed curve represents \(\displaystyle{y}=-{\frac{{{1}}}{{{x}}}}\)
The black solid curve represents \(\displaystyle{y}={1}-{\frac{{{1}}}{{{x}}}}\)