Chapter 8.1, Problem 33PPS

(a)

To determine

To graph the functions for $-1\le x\le 5$ on separate graphs.

Answer to Problem 33PPS

  $\frac{1}{7}=0.\overline{142857}$ , $\frac{6}{7}=0.\overline{857142}$

Explanation of Solution

Given:

The table for the exponential functions are as follows-

  

Calculation:

Graph is obtained using TI-83 calculator as follows:

STEP 1: Start TI-83 calculator.

STEP 2: Press STAT. Press Enter to edit. Enter values of. Screenshot is shown below:

  

STEP 3: Press 2nd STATPLOT. Pres enter. Press On. Screenshot is shown below:

  

STEP 4: Press ZOOM. Press 9. Graph is obtained as shown below:

  

Similarly enter values for the function $g(x)$

Graph is obtained as shown below:

  

Similarly for the function $h(x)$

  

Graph is obtained as follows:

  

(b)

To determine

To find which function has negative coefficient.

Answer to Problem 33PPS

  $f(x)$

Explanation of Solution

An exponential function with negative coefficient is $f(x)$ . Since, it has negative values for positive values of x.

(c)

To determine

To find which function is translated to the left.

Answer to Problem 33PPS

  $h(x)$

Explanation of Solution

Given:

The function $h(x)$ is translated to the left. Change in y-axis is higher when x value is low and change in y-axis is lower when x value is high. Hence this is a translated function.

(d)

To determine

To find which functions are growth models and which are decay models.

Explanation of Solution

Given:

Function $g(x)$ is an exponential growth model because its value increases with increase in x. Functions $f(x)$ and $h(x)$ are exponential decay functions as its value decreases with increase in x.