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The function [tex]$f$[/tex] is given by the table of values shown below:
[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\hline
$x$ & 0 & 1 & 2 & 3 \\
\hline
$f(x)$ & 0 & 2 & 8 & 26 \\
\hline
\end{tabular}
\][/tex]

If function [tex]$f$[/tex] is shifted vertically down by 2 units to obtain function [tex]$g$[/tex], complete the table of values which represents function [tex]$g$[/tex]:
[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\hline
$x$ & 0 & 1 & 2 & 3 \\
\hline
$g(x)$ & \boxed{-2} & \boxed{0} & \boxed{6} & \boxed{24} \\
\hline
\end{tabular}
\][/tex]

Sagot :

GinnyAnswer
To find the values of [tex]\( g(x) \)[/tex] when the function [tex]\( f(x) \)[/tex] is shifted vertically down by 2 units, we need to subtract 2 from each value of [tex]\( f(x) \)[/tex].

Given the table of values for [tex]\( f(x) \)[/tex]:

[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & 0 & 1 & 2 & 3 \\ \hline f(x) & 0 & 2 & 8 & 26 \\ \hline \end{array} \][/tex]

The corresponding [tex]\( g(x) \)[/tex] values can be calculated as follows:

1. For [tex]\( x = 0 \)[/tex]:
[tex]\[ f(0) = 0 \\ g(0) = f(0) - 2 = 0 - 2 = -2 \][/tex]

2. For [tex]\( x = 1 \)[/tex]:
[tex]\[ f(1) = 2 \\ g(1) = f(1) - 2 = 2 - 2 = 0 \][/tex]

3. For [tex]\( x = 2 \)[/tex]:
[tex]\[ f(2) = 8 \\ g(2) = f(2) - 2 = 8 - 2 = 6 \][/tex]

4. For [tex]\( x = 3 \)[/tex]:
[tex]\[ f(3) = 26 \\ g(3) = f(3) - 2 = 26 - 2 = 24 \][/tex]

Thus, the table of values for [tex]\( g(x) \)[/tex] is:

[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & 0 & 1 & 2 & 3 \\ \hline g(x) & -2 & 0 & 6 & 24 \\ \hline \end{array} \][/tex]
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