Question

1. select 2 different colors to sketch the graphs below

$y = 3(2)^{x}$
$y = 3\left(\frac{1}{2}\
ight)^{x}$

Explanation:

Step1: Calculate y for \( y = 3(2)^x \)

For \( x = -2 \): \( y = 3(2)^{-2} = 3\times\frac{1}{4} = \frac{3}{4} = 0.75 \)
For \( x = -1 \): \( y = 3(2)^{-1} = 3\times\frac{1}{2} = \frac{3}{2} = 1.5 \)
For \( x = 0 \): \( y = 3(2)^{0} = 3\times1 = 3 \)
For \( x = 1 \): \( y = 3(2)^{1} = 3\times2 = 6 \)
For \( x = 2 \): \( y = 3(2)^{2} = 3\times4 = 12 \)

Step2: Calculate y for \( y = 3(\frac{1}{2})^x \)

For \( x = -2 \): \( y = 3(\frac{1}{2})^{-2} = 3\times4 = 12 \)
For \( x = -1 \): \( y = 3(\frac{1}{2})^{-1} = 3\times2 = 6 \)
For \( x = 0 \): \( y = 3(\frac{1}{2})^{0} = 3\times1 = 3 \)
For \( x = 1 \): \( y = 3(\frac{1}{2})^{1} = 3\times\frac{1}{2} = 1.5 \)
For \( x = 2 \): \( y = 3(\frac{1}{2})^{2} = 3\times\frac{1}{4} = 0.75 \)

Answer:

For \( y = 3(2)^x \):

x	y
-1	1.5
0	3
1	6
2	12

For \( y = 3(\frac{1}{2})^x \):

x	y
-1	6
0	3
1	1.5
2	0.75

(After filling the tables, you can use the points to sketch the graphs on the coordinate plane with two different colors, one for each function.)