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.
