Question

23–36 ■ 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.

\(y = \sqrt {x - 2} - 1\)

Short answer

The plot of the function \(y = \sqrt {x - 2} - 1\) is

Step-by-step solution

Given data

The function to be plotted is

\(y = \sqrt {x - 2} - 1\)

Plot of the function \(y = \sqrt x \)

The plot of the function \(y = \sqrt x \) is as follows

Figure 1

Plot of the function \(y = \sqrt {x - 2}  - 1\)

The plot of the function \(y = \sqrt {x - 2} \) can be obtained by shifting Figure 1 two units to the right as follows

Figure 2

The plot of the function \(y = \sqrt {x - 2} - 1\) can be obtained by shifting Figure 2 one unit to the bottom as follows

Figure 3