Chapter 6.3, Problem 30E

To determine

To draw: Graph the function. Compare the graph of the parent function. Describe the domain and range of $f.$

  $f(x)=\frac{3}{2}{(0.25)}^x$

Answer to Problem 30E

Domain of the function is $x\in R$

Range of the function is $y\in (0,\infty )$

Explanation of Solution

Given information: The given function is $f(x)=\frac{3}{2}{(0.25)}^x$

Calculation: By putting different values of $x$ we get different values of function so that we can plot the graph.

$x$	-2	-1	0	1	2
$f(x)$	24	6	1.5	0.375	0.094

Using above table we plot the graph

  

From the given function we can find the parent function of given function, the given function is three by two of parent function.

Let $g(x)$ denotes the parent function

  $g(x)={(0.25)}^x$ is the parent function of given function.

Now we plot the graph for both the functions using same way

  

From the graph we can see that domain of the function $f$ is all real values of $x$ . i.e.

  $x\in R$

From the graph we can see that range of the function $f$ is all positive values of $y$ . i.e.

  $y\in (0,\infty )$