Chapter 3, Problem 2PS

To determine

To graph: The functions $y_1=e^x,y_2=x^2,y_3=x^3,y_4=\sqrt{x}\text{ and }{y}_5=\left|x\right|$ also interpret the function that increases at the greatest rate when xapproach $\infty$ .

Explanation of Solution

Given information:

The functions $y_1=e^x,y_2=x^2,y_3=x^3,y_4=\sqrt{x}\text{ and }{y}_5=\left|x\right|$ .

Graph:

Consider the function $y_1=e^x,y_2=x^2,y_3=x^3,y_4=\sqrt{x}\text{ and }{y}_5=\left|x\right|$ . Sketch the functions in a graphing function.

To sketch the function $y_1=e^x$ .

Step 1: Press $\boxed{Y=}$ key.

Step 2: Enter the function, press $\boxed{\text{2nd}}$ key and then $\boxed{\text{LN}}$ key. Write the function $e^\left(x\right)$ .

Step 3: Press the $\boxed{\text{GRAPH}}$ key.

The result obtained on screen is provided below,

  

To sketch the function $y_2=x^2$ .

Step 1: Press $\boxed{Y=}$ key.

Step 2: Enter the function $x^\left(2\right)$ .

Step 3: Press the $\boxed{\text{GRAPH}}$ key.

The result obtained on screen is provided below,

  

To sketch the function $y_3=x^3$ .

Step 1: Press $\boxed{Y=}$ key.

Step 2: Enter the function $x^\left(3\right)$ .

Step 3: Press the $\boxed{\text{GRAPH}}$ key.

The result obtained on screen is provided below,

  

To sketch the function $y_4=\sqrt{x}$ .

Step 1: Press $\boxed{Y=}$ key.

Step 2: Enter the function,press $\boxed{\text{2nd}}$ key and then $\boxed{x^2}$ key. Write the function $\sqrt{x}$ .

Step 3: Press the $\boxed{\text{GRAPH}}$ key.

The result obtained on screen is provided below,

  

To sketch the function $y_2=\left|x\right|$ .

Step 1: Press $\boxed{Y=}$ key.

Step 2: Enter the function, press $\boxed{\text{MATH}}$ key under the $\boxed{\text{NUM}}$ tab choose the first option that is $\boxed{\text{abs}(}$ function. Write the function $\text{abs}\left(x\right)$ .

Step 3: Press the $\boxed{\text{GRAPH}}$ key.

The result obtained on screen is provided below,

  

Interpretation:

When $x=100$ , the values obtained by the functions $y_1=e^x,y_2=x^2,y_3=x^3,y_4=\sqrt{x}\text{ and }{y}_5=\left|x\right|$ are as follows. $y_1=2.6\times {10}^{43},y_2=10000,y_3=1000000,y_4=10\text{ and }{y}_5=100$ . The exponential function $y_1=e^x$ increases rapidly as x approaches infinity.