Chapter 8, Problem 7CR

(a)

To determine

To graph: The function $y=e^x$ over the interval $\left[0,4\right]$

Explanation of Solution

Given information:

The function $y=e^x$ over the interval $\left[0,4\right]$

Graph:

To graph the function $y=e^x$ using graphing utility, use below steps

Step I: Press the ON key.

Step II: Now, press [Y=]. Input the right hand side of the function $y=e^x$ in $Y_1$

Step III: Press [WINDOW] key and set the viewing window as below,

  $\begin{array}{ll}X\min =0\hfill & X\max =4\hfill \\ Y\min =1\hfill & Y\max =e^4\hfill \end{array}$

Step IV: Then, hit [Graph] key to view the graph.

The graph of the function is as follows:

  

Interpretation:

The graph represents function of $y=e^x$

(b)

To determine

To graph: The function $y=\sin x$ over the interval $\left[0,4\right]$

Explanation of Solution

Given information:

The function $y=\sin x$ over the interval $\left[0,4\right]$

Graph:

To graph the function $y=\sin x$ using graphing utility, use below steps

Step I: Press the ON key.

Step II: Now, press [Y=]. Input the right hand side of the function $y=\sin x$ in $Y_1$

Step III: Press [WINDOW] key and set the viewing window as below

  $\begin{array}{ll}X\min =0\hfill & X\max =4\hfill \\ Y\min =-1\hfill & Y\max =1\hfill \end{array}$

Step IV: Then, hit [Graph] key to view the graph.

The graph of the function is as follows:

  

Interpretation:

The graph represents function of $y=\sin x$

(c)

To determine

To graph: The function $y=e^x\sin x$ over the interval $\left[0,4\right]$

Explanation of Solution

Given information:

The function $y=e^x\sin x$ over the interval $\left[0,4\right]$

Graph:

To graph the function $y=e^x\sin x$ using graphing utility, use below steps

Step I: Press the ON key.

Step II: Now, press [Y=]. Input the right hand side of the function $y=e^x\sin x$ in $Y_1$

Step III: Press [WINDOW] key and set the viewing window as below,

  $\begin{array}{ll}X\min =0\hfill & X\max =4\hfill \\ Y\min =-45\hfill & Y\max =8\hfill \end{array}$

Step IV: Then, hit [Graph] key to view the graph.

The graph of the function is as follows:

  

Interpretation:

The graph represents function of $y=e^x\sin x$

(d)

To determine

To graph: The function $y=2x+\sin x$ over the interval $\left[0,4\right]$

Explanation of Solution

Given information:

The function, $y=2x+\sin x$ over the interval $\left[0,4\right]$

Graph:

To graph the function $y=2x+\sin x$ using graphing utility, use below steps

Step I: Press the ON key.

Step II: Now, press [Y=]. Input the right hand side of the function $y=2x+\sin x$ in $Y_1$

Step III: Press [WINDOW] key and set the viewing window as below,

  $\begin{array}{ll}X\min =0\hfill & X\max =4\hfill \\ Y\min =-2\hfill & Y\max =8\hfill \end{array}$

Step IV: Then, hit [Graph] key to view the graph

The graph of the function is as follows:

  

Interpretation:

The graph represents function of $y=2x+\sin x$