Answer :
To complete the input-output table for the function [tex]\( y = 3^x \)[/tex], let's follow the function step-by-step for the given values of [tex]\( x \)[/tex]:
Given the function [tex]\( y = 3^x \)[/tex]:
1. For [tex]\( x = -2 \)[/tex]:
[tex]\[ y = 3^{-2} = \frac{1}{3^2} = \frac{1}{9} \][/tex]
2. For [tex]\( x = -1 \)[/tex]:
[tex]\[ y = 3^{-1} = \frac{1}{3^1} = \frac{1}{3} \][/tex]
3. For [tex]\( x = 0 \)[/tex]:
[tex]\[ y = 3^0 = 1 \][/tex]
4. For [tex]\( x = 1 \)[/tex]:
[tex]\[ y = 3^1 = 3 \][/tex]
5. For [tex]\( x = 2 \)[/tex]:
[tex]\[ y = 3^2 = 9 \][/tex]
6. For [tex]\( x = 3 \)[/tex]:
[tex]\[ y = 3^3 = 27 \][/tex]
7. For [tex]\( x = 4 \)[/tex]:
[tex]\[ y = 3^4 = 81 \][/tex]
As a result, we now have the values for [tex]\( y \)[/tex] when [tex]\( x = 3 \)[/tex] and [tex]\( x = 4 \)[/tex]. Thus, [tex]\( a = 27 \)[/tex] and [tex]\( b = 81 \)[/tex]:
[tex]\[ \begin{array}{|r|r|} \hline x & y \\ \hline -2 & \frac{1}{9} \\ \hline -1 & \frac{1}{3} \\ \hline 0 & 1 \\ \hline 1 & 3 \\ \hline 2 & 9 \\ \hline 3 & 27 \\ \hline 4 & 81 \\ \hline \end{array} \][/tex]
Therefore:
[tex]\[ a = 27 \quad \text{and} \quad b = 81 \][/tex]
Given the function [tex]\( y = 3^x \)[/tex]:
1. For [tex]\( x = -2 \)[/tex]:
[tex]\[ y = 3^{-2} = \frac{1}{3^2} = \frac{1}{9} \][/tex]
2. For [tex]\( x = -1 \)[/tex]:
[tex]\[ y = 3^{-1} = \frac{1}{3^1} = \frac{1}{3} \][/tex]
3. For [tex]\( x = 0 \)[/tex]:
[tex]\[ y = 3^0 = 1 \][/tex]
4. For [tex]\( x = 1 \)[/tex]:
[tex]\[ y = 3^1 = 3 \][/tex]
5. For [tex]\( x = 2 \)[/tex]:
[tex]\[ y = 3^2 = 9 \][/tex]
6. For [tex]\( x = 3 \)[/tex]:
[tex]\[ y = 3^3 = 27 \][/tex]
7. For [tex]\( x = 4 \)[/tex]:
[tex]\[ y = 3^4 = 81 \][/tex]
As a result, we now have the values for [tex]\( y \)[/tex] when [tex]\( x = 3 \)[/tex] and [tex]\( x = 4 \)[/tex]. Thus, [tex]\( a = 27 \)[/tex] and [tex]\( b = 81 \)[/tex]:
[tex]\[ \begin{array}{|r|r|} \hline x & y \\ \hline -2 & \frac{1}{9} \\ \hline -1 & \frac{1}{3} \\ \hline 0 & 1 \\ \hline 1 & 3 \\ \hline 2 & 9 \\ \hline 3 & 27 \\ \hline 4 & 81 \\ \hline \end{array} \][/tex]
Therefore:
[tex]\[ a = 27 \quad \text{and} \quad b = 81 \][/tex]