Let's fill in the function table step-by-step for the function [tex]\( f(x) = 2x - 5 \)[/tex].
1. For [tex]\( x = -1 \)[/tex]:
[tex]\[
f(-1) = 2(-1) - 5
= -2 - 5
= -7
\][/tex]
So, [tex]\( f(-1) = -7 \)[/tex].
2. For [tex]\( x = 0 \)[/tex]:
[tex]\[
f(0) = 2(0) - 5
= 0 - 5
= -5
\][/tex]
So, [tex]\( f(0) = -5 \)[/tex].
3. For [tex]\( x = 1 \)[/tex]:
[tex]\[
f(1) = 2(1) - 5
= 2 - 5
= -3
\][/tex]
So, [tex]\( f(1) = -3 \)[/tex].
4. For [tex]\( x = 2 \)[/tex]:
[tex]\[
f(2) = 2(2) - 5
= 4 - 5
= -1
\][/tex]
So, [tex]\( f(2) = -1 \)[/tex].
5. For [tex]\( x = 3 \)[/tex]:
[tex]\[
f(3) = 2(3) - 5
= 6 - 5
= 1
\][/tex]
So, [tex]\( f(3) = 1 \)[/tex].
Now we can complete the function table:
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-1 & -7 \\
\hline
0 & -5 \\
\hline
1 & -3 \\
\hline
2 & -1 \\
\hline
3 & 1 \\
\hline
\end{array}
\][/tex]
