Complete the missing parts of the table for the following function.

[tex]\[ y = 5^x \][/tex]

\begin{tabular}{c|cccccc}
x & -2 & -1 & 0 & 1 & 2 & 3 \\
\hline
y & [tex]$\frac{1}{25}$[/tex] & [tex]$\frac{1}{5}$[/tex] & 1 & 5 & 25 & 125 \\
\end{tabular}



Answer :

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]