Chapter 7.6, Problem 20P

Evaluate each function over the domain $\{-2,-1,0,1,2,3\}.$

As the values of the domain increase, do the values of the range increase or decrease?

$g(t)=4\cdot 3^x$

To determine

To evaluate: The given function $g\left(t\right)$ over the certain domain $D=\left\{-2,-1,0,1,2,3\right\}$ and determine as the values of domain increase, do the values of range increase or decrease.

Answer to Problem 20P

As the values of domain of function $g\left(t\right)=4\cdot 3^x$ increase the values of range increase.

Explanation of Solution

Given information:

The given function is $g\left(t\right)=4\cdot 3^x$ and given domain $\left\{-2,-1,0,1,2,3\right\}$ .

Method used:

The range of function is determine using calculating values of function for $x\in \left\{-2,-1,0,1,2,3\right\}$ .

Calculations:

The values of function $g\left(t\right)=4\cdot 3^x$ or the range of function $g\left(t\right)$ for $x\in \left\{-2,-1,0,1,2,3\right\}$ are given in following table.

x	Range of g ( t )
-2	0.444
-1	1.333
0	4.000
1	12.000
2	36.000
3	108.000

From the table it is clear that as the values of domain increase the values of range increase.

Conclusion:

As the values of domain of function $g\left(t\right)=4\cdot 3^x$ increase the values of range increase.