Sure, let's complete the missing parts of the table for the function [tex]\( y = 5^x \)[/tex].
Given the table:
[tex]\[
\begin{array}{c|cccccc}
x & -2 & -1 & 0 & 1 & 2 & 3 \\
\hline
y & \frac{1}{25} & \frac{1}{[?]} & 1 & 5 & [?] & [?]
\end{array}
\][/tex]
We need to determine the values of [tex]\( y \)[/tex] for [tex]\( x = -1 \)[/tex], [tex]\( x = 2 \)[/tex], and [tex]\( x = 3 \)[/tex].
1. For [tex]\( x = -1 \)[/tex]:
[tex]\[ y = 5^{-1} = \frac{1}{5} \][/tex]
So, the missing value [tex]\( \frac{1}{[?]} \)[/tex] is [tex]\( \frac{1}{5} \)[/tex].
2. For [tex]\( x = 2 \)[/tex]:
[tex]\[ y = 5^2 = 25 \][/tex]
So, the missing value [tex]\( [?] \)[/tex] for [tex]\( x = 2 \)[/tex] is [tex]\( 25 \)[/tex].
3. For [tex]\( x = 3 \)[/tex]:
[tex]\[ y = 5^3 = 125 \][/tex]
So, the missing value [tex]\( [?] \)[/tex] for [tex]\( x = 3 \)[/tex] is [tex]\( 125 \)[/tex].
Now the completed table is:
[tex]\[
\begin{array}{c|cccccc}
x & -2 & -1 & 0 & 1 & 2 & 3 \\
\hline
y & \frac{1}{25} & \frac{1}{5} & 1 & 5 & 25 & 125
\end{array}
\][/tex]
