The table represents the function [tex]$f(x) = 5x$[/tex].

\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$f(x)$[/tex] \\
\hline
-1 & \\
\hline
0 & 0 \\
\hline
1 & 5 \\
\hline
2 & 10 \\
\hline
\end{tabular}

Which value goes in the empty cell?

A. [tex]$-5$[/tex]
B. [tex]$-51$[/tex]
C. 5
D. 51



Answer :

To determine the value that goes in the empty cell for the function [tex]\( f(x) = 5x \)[/tex] when [tex]\( x = -1 \)[/tex], follow these steps:

1. Notice that the function provided is [tex]\( f(x) = 5x \)[/tex]. This means that for any given value of [tex]\( x \)[/tex], the function [tex]\( f(x) \)[/tex] is calculated by multiplying [tex]\( x \)[/tex] by 5.
2. To find the value of [tex]\( f(x) \)[/tex] when [tex]\( x = -1 \)[/tex]:
[tex]\[ f(-1) = 5 \times (-1) \][/tex]
3. Perform the multiplication:
[tex]\[ f(-1) = -5 \][/tex]

Thus, the value that belongs in the empty cell for [tex]\( f(x) \)[/tex] when [tex]\( x = -1 \)[/tex] is [tex]\(-5\)[/tex].

The correct answer is [tex]\(-5\)[/tex].

[tex]\[ \boxed{-5} \][/tex]