Complete the table for the function y= 2(1/3)^x.

Question

Complete the table for the function y= 2(1/3)^x.
x y
–2
–1
0
1
Now, graph the function.
Plot two points to graph the function.

GPT-4o mini · Answer

To complete the table for the function $ y = 2(1/3)^x $, let's calculate the values of $ y $ for the given values of $ x $. ### Compute Values 1. For $ x = -2 $: $$ y = 2 \left( \frac{1}{3} \right)^{-2} = 2 \cdot 3^2 = 2 \cdot 9 = 18 $$ 2. For $ x = -1 $: $$ y = 2 \left( \frac{1}{3} \right)^{-1} = 2 \cdot 3^1 = 2 \cdot 3 = 6 $$ 3. For $ x = 0 $: $$ y = 2 \left( \frac{1}{3} \right)^{0} = 2 \cdot 1 = 2 $$ 4. For $ x = 1 $: $$ y = 2 \left( \frac{1}{3} \right)^{1} = 2 \cdot \frac{1}{3} = \frac{2}{3} $$ ### Complete the Table | x | y | |-----|-----| | -2 | 18 | | -1 | 6 | | 0 | 2 | | 1 | $ \frac{2}{3} $ | ### Plotting the Points Now, let's plot the points based on the table: 1. Point for $ x = -2 $: $ (-2, 18) $ 2. Point for $ x = -1 $: $ (-1, 6) $ 3. Point for $ x = 0 $: $ (0, 2) $ 4. Point for $ x = 1 $: $ (1, \frac{2}{3}) $ ### Graph To graph the function: - Start by plotting the points $ (-2, 18) $, $ (-1, 6) $, $ (0, 2) $, and $ (1, \frac{2}{3}) $. - The function $ y = 2(1/3)^x $ will show a decreasing trend as $ x $ increases, suggesting an exponential decay. If you were to sketch the graph, it would start from a high value when $ x $ is negative and decrease as $ x $ increases, approaching the x-axis but never quite touching it.