Chapter 6.4, Problem 11Q

To determine

To sketch:The graph of the function and describe the domain and range.

Answer to Problem 11Q

The graph of the given function is drawn in blue color in the following graph:

  

The domain is all real numbers and the range is $y>-1$ .

Explanation of Solution

Giveninformation:

The function is $f(x)=6{(2)}^{x-4}-1$

To graph the function, let’s begin by graphing $y=6{(2)}^x$ . For this, we prepare the table values as follows:

$x$	$-2$	$-1$	0	1	2
$f(x)$	$\frac{3}{2}$	3	6	12	24

Now, plotting the ordered points and drawing a smooth curve through the points, we obtain:

  

Now, shift the graph by 4 units to the right and down the graph by 1 unit to obtain the graph of the given function. That is,

  

Conclusion:

From the graph, we can observe that the graph of the function approaches the line $y=-1$ but not intersect it. Therefore, the domain is all real numbers and the range is $y>-1$ .