Chapter 11.2, Problem 17E

To determine

To graph: the given exponential function or inequality.

Answer to Problem 17E

Explanation of Solution

Given:

The given function $y\le {\left(\frac{1}{2}\right)}^x$ .

Calculation:

First graph the function $y\le {\left(\frac{1}{2}\right)}^x$ .

Create a table to use some points for the graph.

$x$	${\left(\frac{1}{2}\right)}^x$
$-2$	$4$
$-1$	$2$
$0$	$1$
$1$	$0.5$
$2$	$0.25$

use the origin as a test point

  ${\left(\frac{1}{2}\right)}^0=1>0$

conclude that the origin belongs to the solution and therefore the yellow region is the solution.

Thegraph of $y\le {\left(\frac{1}{2}\right)}^x$ is shown below: