Chapter 1.3, Problem 17E

To determine

To sketch: The function $y=\sqrt{x}$ by hand without plotting any points and then graph of the function $y=2-\sqrt{x}$.

Explanation of Solution

The standard graph of the function $y=\sqrt{x}$ is roughly drawn as shown below in Figure 1.

Then, draw the graph of $y=-\sqrt{x}$ by reflecting the graph $y=\sqrt{x}$ about x-axis as it is an odd function. Thus, the graph of $y=-\sqrt{x}$ is shown below in Figure 2.

From Figure 2, it is observed that Figure 1 is reflected about the origin.

To draw the graph of $y=2-\sqrt{x}$, shift the graph $y=-\sqrt{x}$ by 2 units upward. Thus, the graph of $y=2-\sqrt{x}$ is shown below in Figure 3.

Observe that Figure 3is obtainedfrom Figure 1 in such a way that it is reflected about the x-axis and then shifted 2 units upward.