Question

complete the table of values for the following exponential functions. use a different color for each function.

x	-3	-2	-1	0	1	2	3
$g(x)=2^{x - 2}$	$\frac{1}{32}$	$\frac{1}{16}$	$\frac{1}{8}$
$h(x)=2^{x + 2}$				1

Explanation:

Step1: Calculate $g(x)$ for $x=0$

Substitute $x=0$ into $g(x)=2^{x-2}$:
$g(0)=2^{0-2}=2^{-2}=\frac{1}{2^2}=\frac{1}{4}$

Step2: Calculate $g(x)$ for $x=1$

Substitute $x=1$ into $g(x)=2^{x-2}$:
$g(1)=2^{1-2}=2^{-1}=\frac{1}{2^1}=\frac{1}{2}$

Step3: Calculate $g(x)$ for $x=2$

Substitute $x=2$ into $g(x)=2^{x-2}$:
$g(2)=2^{2-2}=2^{0}=1$

Step4: Calculate $g(x)$ for $x=3$

Substitute $x=3$ into $g(x)=2^{x-2}$:
$g(3)=2^{3-2}=2^{1}=2$

Step5: Calculate $h(x)$ for $x=-3$

Substitute $x=-3$ into $h(x)=2^{x+2}$:
$h(-3)=2^{-3+2}=2^{-1}=\frac{1}{2^1}=\frac{1}{2}$

Step6: Calculate $h(x)$ for $x=-2$

Substitute $x=-2$ into $h(x)=2^{x+2}$:
$h(-2)=2^{-2+2}=2^{0}=1$

Step7: Calculate $h(x)$ for $x=-1$

Substitute $x=-1$ into $h(x)=2^{x+2}$:
$h(-1)=2^{-1+2}=2^{1}=2$

Step8: Calculate $h(x)$ for $x=1$

Substitute $x=1$ into $h(x)=2^{x+2}$:
$h(1)=2^{1+2}=2^{3}=8$

Step9: Calculate $h(x)$ for $x=2$

Substitute $x=2$ into $h(x)=2^{x+2}$:
$h(2)=2^{2+2}=2^{4}=16$

Step10: Calculate $h(x)$ for $x=3$

Substitute $x=3$ into $h(x)=2^{x+2}$:
$h(3)=2^{3+2}=2^{5}=32$

Answer:

Completed table values:

$x$	$f(x)=2^x$	$g(x)=2^{x-2}$	$h(x)=2^{x+2}$
$-2$	$\frac{1}{4}$	$\frac{1}{16}$	$1$
$-1$	$\frac{1}{2}$	$\frac{1}{8}$	$2$
$0$	$1$	$\frac{1}{4}$	$1$
$1$	$2$	$\frac{1}{2}$	$8$
$2$	$4$	$1$	$16$
$3$	$8$	$2$	$32$