Question

■ 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.

30. \(y = \frac{2}{x} - 2\)

Short answer

The plot of the function \(y = \frac{2}{x} - 2\) is

Step-by-step solution

Given data

The function to be plotted is

\(y = \frac{2}{x} - 2\)

Plot of the function \(y = \frac{1}{x}\)

The plot of the function \(y = \frac{1}{x}\) is as follows

Plot of the function \(y = \frac{2}{x} - 2\)

The plot of the function \(y = \frac{2}{x}\) can be obtained by scaling up Figure 1 by 2 as follows

The plot of the function \(y = \frac{2}{x} - 2\) can be obtained by shifting Figure 2 by 2 downwards as follows