given the function below, fill in the table of values, use the table of values to graph the function, and…

Explanation:

Step1: Calculate $\left(\frac{1}{2}\right)^x$ for $x=-3$

$\left(\frac{1}{2}\right)^{-3} = 2^3 = 8$

Step2: Calculate $y$ for $x=-3$

$y = 8 - 1 = 7$

Step3: Calculate $\left(\frac{1}{2}\right)^x$ for $x=-2$

$\left(\frac{1}{2}\right)^{-2} = 2^2 = 4$

Step4: Calculate $y$ for $x=-2$

$y = 4 - 1 = 3$

Step5: Calculate $\left(\frac{1}{2}\right)^x$ for $x=-1$

$\left(\frac{1}{2}\right)^{-1} = 2^1 = 2$

Step6: Calculate $y$ for $x=-1$

$y = 2 - 1 = 1$

Step7: Calculate $\left(\frac{1}{2}\right)^x$ for $x=0$

$\left(\frac{1}{2}\right)^0 = 1$

Step8: Calculate $y$ for $x=0$

$y = 1 - 1 = 0$

Step9: Calculate $\left(\frac{1}{2}\right)^x$ for $x=1$

$\left(\frac{1}{2}\right)^1 = \frac{1}{2}$

Step10: Calculate $y$ for $x=1$

$y = \frac{1}{2} - 1 = -\frac{1}{2}$

Step11: Calculate $\left(\frac{1}{2}\right)^x$ for $x=2$

$\left(\frac{1}{2}\right)^2 = \frac{1}{4}$

Step12: Calculate $y$ for $x=2$

$y = \frac{1}{4} - 1 = -\frac{3}{4}$

Step13: Identify domain of the function

Exponential functions accept all real numbers as inputs, so the domain is all real $x$.

Step14: Identify range of the function

$\left(\frac{1}{2}\right)^x > 0$ for all real $x$, so $\left(\frac{1}{2}\right)^x - 1 > -1$.

Answer:

Completed Table:

$x$	$\left(\frac{1}{2}\right)^x$	$y = \left(\frac{1}{2}\right)^x - 1$
$-3$	$8$	$7$
$-2$	$4$	$3$
$-1$	$2$	$1$
$0$	$1$	$0$
$1$	$\frac{1}{2}$	$-\frac{1}{2}$
$2$	$\frac{1}{4}$	$-\frac{3}{4}$

Domain and Range:

• Domain: All real numbers, or $(-\infty, \infty)$
• Range: All real numbers greater than $-1$, or $(-1, \infty)$