Question

given the function below, fill in the table of values, use the table of values to graph the function, and then identify the functions domain and range.
$y = 2^x + 1$

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

you must answer all questions above in order to submit.

Explanation:

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

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

Step2: Calculate $y=2^x+1$ for each $x$

For $x=-2$: $y=\frac{1}{4}+1=\frac{5}{4}$
For $x=-1$: $y=\frac{1}{2}+1=\frac{3}{2}$
For $x=0$: $y=1+1=2$
For $x=1$: $y=2+1=3$
For $x=2$: $y=4+1=5$
For $x=3$: $y=8+1=9$

Step3: Identify domain of $y=2^x+1$

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

Step4: Identify range of $y=2^x+1$

$2^x>0$ for all real $x$, so $2^x+1>1$. Range is all real $y>1$.

Answer:

Completed Table:

$x$	$2^x$	$y=2^x+1$
$-1$	$\frac{1}{2}$	$\frac{3}{2}$
$0$	$1$	$2$
$1$	$2$	$3$
$2$	$4$	$5$
$3$	$8$	$9$

Domain and Range:

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