Chapter B, Problem 1E

To determine

To find:

The most appropriate viewing rectangle for the equation $y=x^4+2$.

Answer to Problem 1E

The most appropriate viewing rectangle for the equation $y=x^4+2$ is $\left[-8,8\right]\text{ by }\left[-4,40\right]$.

Explanation of Solution

Given information:

The equation is $y=x^4+2$.

Graph:

The given equation is $y=x^4+2$.

To graph the equation $y=x^4+2$, first turn ON the calculator, then press the button Y= and insert the equation as shown in Figure 1.

Now, press the WINDOW button and set the viewing window $\left[-2,2\right]$ by $\left[-2,2\right]$ as shown in Figure 2.

After this press the GRAPH button and the graph is obtained as shown in Figure 3.

It can be seen from the Figure 3 that the viewing window $\left[-2,2\right]$ by $\left[-2,2\right]$ in the graph is not appropriate for the equation $y=x^4+2$.

Now, press the WINDOW button and set the viewing window $\left[0,4\right]$ by $\left[0,4\right]$ as shown in Figure 4.

After this press the GRAPH button and the graph is obtained as shown in Figure 5.

It can be seen from the Figure 5 that the viewing window $\left[0,4\right]$ by $\left[0,4\right]$ in the graph is not appropriate for the equation $y=x^4+2$.

Now, press the WINDOW button and set the viewing window $\left[-8,8\right]$ by $\left[-4,40\right]$ as shown in Figure 6.

After this press the GRAPH button and the graph is obtained as shown in Figure 7.

It can be seen from the Figure 7 that the viewing window $\left[-8,8\right]$ by $\left[-4,40\right]$ in the graph is appropriate for the equation $y=x^4+2$.

Now, press the WINDOW button and set the viewing window $\left[-40,40\right]$ by $\left[-80,800\right]$ as shown in Figure 8.

After this press the GRAPH button and the graph is obtained as shown in Figure 9.

It can be seen from the Figure 9 that the viewing window $\left[-40,40\right]$ by $\left[-80,800\right]$ in the graph is not appropriate for the equation $y=x^4+2$.

Conclusion:

Thus, the most appropriate viewing rectangle for the equation $y=x^4+2$ is $\left[-8,8\right]\text{ by }\left[-4,40\right]$.