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Complete the function table for the given equation:

[tex]\[
f(x) = 4|x| - 1
\][/tex]

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



Answer :

GinnyAnswer
Alright, let's complete the function table given the function [tex]\( f(x) = 4|x| - 1 \)[/tex]. I'll guide you through each step for finding [tex]\( f(x) \)[/tex] using the given [tex]\( x \)[/tex]-values.

1. When [tex]\( x = -1 \)[/tex]:
[tex]\[ f(-1) = 4| -1 | - 1 \][/tex]
Absolute value of [tex]\(-1\)[/tex] is 1.
[tex]\[ f(-1) = 4 \cdot 1 - 1 = 4 - 1 = 3 \][/tex]

2. When [tex]\( x = 0 \)[/tex]:
[tex]\[ f(0) = 4| 0 | - 1 \][/tex]
Absolute value of [tex]\(0\)[/tex] is 0.
[tex]\[ f(0) = 4 \cdot 0 - 1 = 0 - 1 = -1 \][/tex]

3. When [tex]\( x = 1 \)[/tex]:
[tex]\[ f(1) = 4| 1 | - 1 \][/tex]
Absolute value of [tex]\(1\)[/tex] is 1.
[tex]\[ f(1) = 4 \cdot 1 - 1 = 4 - 1 = 3 \][/tex]

4. When [tex]\( x = 2 \)[/tex]:
[tex]\[ f(2) = 4| 2 | - 1 \][/tex]
Absolute value of [tex]\(2\)[/tex] is 2.
[tex]\[ f(2) = 4 \cdot 2 - 1 = 8 - 1 = 7 \][/tex]

So, the completed table should look like this:
[tex]\[ \begin{tabular}{|c|c|} \hline$f(x)=4|x|-1$ \\ \hline$x$ & $f(x)$ \\ \hline-1 & 3 \\ \hline 0 & -1 \\ \hline 1 & 3 \\ \hline 2 & 7 \\ \hline \end{tabular} \][/tex]

This table now provides the values of the function [tex]\( f(x) = 4|x| - 1 \)[/tex] for the given [tex]\( x \)[/tex]-values.

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