Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions, and then applying the appropriate transformations. y=1-frac{1}{x}

Question
Transformations of functions
asked 2021-02-18
Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions, and then applying the appropriate transformations. \(\displaystyle{y}={1}-{\frac{{{1}}}{{{x}}}}\)

Answers (1)

2021-02-19
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 \(\displaystyle{y}=-{\frac{{{1}}}{{{x}}}}\) image 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 \(\displaystyle{y}={1}-{\frac{{{1}}}{{{x}}}}\) image
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