Chapter 1.3, Problem 16E

To determine

To sketch: The function $y=1+\sin \pi x$ by hand without plotting any points.

Explanation of Solution

The standard graph of the function $y=\sin x$ is roughly drawn and shown below in Figure 1.

Draw the graph of $y=\sin \pi x$ by shrinking the graph of $y=\sin x$ horizontally by a factor of $\pi$.

Use online graphing calculator to sketch the graph of $y=\sin \pi x$ as shown below in Figure 2.

From Figure 2, it is observed that Figure 1 is compressed horizontally by a factor of $\pi$.

To draw the graph of $y=1+\sin \pi x$, shift the graph $y=\sin \pi x$ by 1 unit upward.

Use online graphing calculator to sketch the graph of $y=1+\sin \pi x$ as shown below in Figure 3.

From Figure 3, it is observed that the graph of the function $y=1+\sin \pi x$ lies above the x-axis.