Question

given the function below, fill in the table of values, use the table of values to graph the function, and then identify the function’s domain and range.

$y = 2^{x+2}$

$x$	$x + 2$	$y = 2^{x+2}$
$-3$
$-2$
$-1$
$0$
$1$

Explanation:

Step1: Calculate $x+2$ for each $x$

For $x=-4$: $-4+2=-2$
For $x=-3$: $-3+2=-1$
For $x=-2$: $-2+2=0$
For $x=-1$: $-1+2=1$
For $x=0$: $0+2=2$
For $x=1$: $1+2=3$

Step2: Calculate $y=2^{x+2}$ for each value

For $x=-4$: $2^{-2}=\frac{1}{2^2}=\frac{1}{4}$
For $x=-3$: $2^{-1}=\frac{1}{2^1}=\frac{1}{2}$
For $x=-2$: $2^{0}=1$
For $x=-1$: $2^{1}=2$
For $x=0$: $2^{2}=4$
For $x=1$: $2^{3}=8$

Step3: Identify domain of the function

The function $y=2^{x+2}$ is an exponential function, which accepts all real numbers as input for $x$.

Step4: Identify range of the function

Exponential functions of the form $a^{kx+c}$ (where $a>1$) produce only positive real numbers, and the function can take any positive real value as $x$ varies.

Answer:

Completed Table:

$x$	$x+2$	$y=2^{x+2}$
$-3$	$-1$	$\frac{1}{2}$
$-2$	$0$	$1$
$-1$	$1$	$2$
$0$	$2$	$4$
$1$	$3$	$8$

Domain and Range:

• Domain: All real numbers, or $(-\infty, \infty)$
• Range: All positive real numbers, or $(0, \infty)$