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Given the table of values for the original absolute value function [tex]$f(x)$[/tex] and the transformed function [tex]$g(x) = 14 f(x)$[/tex], what is the value of [tex]$g(-3)$[/tex]?

\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$f(x)$[/tex] \\
\hline
-8 & -3 \\
\hline
-3 & 2 \\
\hline
4 & 5 \\
\hline
9 & 0 \\
\hline
14 & -5 \\
\hline
\end{tabular}

A. 28
B. 2
C. [tex]$-8$[/tex]
D. [tex]$-42$[/tex]

Sagot :

GinnyAnswer
To find the value of [tex]\( g(-3) \)[/tex] for the function [tex]\( g(x) = 14 f(x) \)[/tex]:

1. Identify [tex]\( f(-3) \)[/tex] from the table:
- The table provides values of [tex]\( f(x) \)[/tex] corresponding to different [tex]\( x \)[/tex] values.
- From the table, when [tex]\( x = -3 \)[/tex], the value of [tex]\( f(-3) = 2 \)[/tex].

2. Determine the value of [tex]\( g(-3) \)[/tex]:
- Given that [tex]\( g(x) = 14 f(x) \)[/tex], you need to substitute [tex]\( x = -3 \)[/tex] into the equation for [tex]\( g \)[/tex].
- So, [tex]\( g(-3) = 14 f(-3) \)[/tex].

3. Calculate [tex]\( g(-3) \)[/tex]:
- Substitute the previously found [tex]\( f(-3) = 2 \)[/tex] into the equation for [tex]\( g \)[/tex].
- Therefore, [tex]\( g(-3) = 14 \times 2 = 28 \)[/tex].

So, the value of [tex]\( g(-3) \)[/tex] is [tex]\(\boxed{28}\)[/tex].
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