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The function [tex]$f$[/tex] is given by the table of values:
\begin{tabular}{|c|c|c|c|c|}
\hline
[tex]$x$[/tex] & 1 & 2 & 3 & 4 \\
\hline
[tex]$f(x)$[/tex] & 5 & 7 & 9 & 11 \\
\hline
\end{tabular}

If [tex]$f(x)$[/tex] is shifted 5 units down to obtain [tex]$g(x)$[/tex], which table of values represents the function [tex]$g$[/tex]?

A.
\begin{tabular}{|c|c|c|c|c|}
\hline
[tex]$x$[/tex] & 1 & 2 & 3 & 4 \\
\hline
[tex]$g(x)$[/tex] & 10 & 12 & 14 & 16 \\
\hline
\end{tabular}

B.
\begin{tabular}{|c|c|c|c|c|}
\hline
[tex]$x$[/tex] & -4 & -3 & -2 & -1 \\
\hline
[tex]$g(x)$[/tex] & 5 & 7 & 9 & 11 \\
\hline
\end{tabular}

C.
\begin{tabular}{|c|c|c|c|c|}
\hline
[tex]$x$[/tex] & 1 & 2 & 3 & 4 \\
\hline
[tex]$g(x)$[/tex] & 0 & 2 & 4 & 6 \\
\hline
\end{tabular}

D.
\begin{tabular}{|c|c|c|c|c|}
\hline
[tex]$x$[/tex] & -4 & -3 & -2 & -1 \\
\hline
[tex]$g(x)$[/tex] & 0 & 2 & 4 & 6 \\
\hline
\end{tabular}

Sagot :

GinnyAnsweridn
To determine which table represents the function \( g(x) \), given that \( g(x) \) is obtained by shifting \( f(x) \) 5 units down, let's analyze the changes step-by-step.

First, we look at the original values of \( f(x) \):

[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 \\ \hline f(x) & 5 & 7 & 9 & 11 \\ \hline \end{array} \][/tex]

Shifting \( f(x) \) 5 units down means we subtract 5 from each value of \( f(x) \) to get \( g(x) \):

[tex]\[ g(x) = f(x) - 5 \][/tex]

Now, let's perform the subtraction for each \( f(x) \):

[tex]\[ \begin{align*} g(1) &= f(1) - 5 = 5 - 5 = 0 \\ g(2) &= f(2) - 5 = 7 - 5 = 2 \\ g(3) &= f(3) - 5 = 9 - 5 = 4 \\ g(4) &= f(4) - 5 = 11 - 5 = 6 \\ \end{align*} \][/tex]

So, the values of \( g(x) \) are:

[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 \\ \hline g(x) & 0 & 2 & 4 & 6 \\ \hline \end{array} \][/tex]

Comparing this with the provided choices:

A.
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 \\ \hline g(x) & 10 & 12 & 14 & 16 \\ \hline \end{array} \][/tex]

B.
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & -4 & -3 & -2 & -1 \\ \hline g(x) & 5 & 7 & 9 & 11 \\ \hline \end{array} \][/tex]

C.
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 \\ \hline g(x) & 0 & 2 & 4 & 6 \\ \hline \end{array} \][/tex]

D.
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & -4 & -3 & -2 & -1 \\ \hline g(x) & 0 & 2 & 4 & 6 \\ \hline \end{array} \][/tex]

The correct choice that matches our calculated values is:

Choice C.
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 \\ \hline g(x) & 0 & 2 & 4 & 6 \\ \hline \end{array} \][/tex]
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