To understand and analyze the function [tex]\( g \)[/tex], we need to examine its values at various points [tex]\( x \)[/tex] as provided in the table. Let's go through each [tex]\( x \)[/tex] value and match it with its corresponding [tex]\( g(x) \)[/tex] value.
Here's the table with the values filled in:
[tex]\[
\begin{tabular}{|c|c|}
\hline
x & g(x) \\
\hline
-2 & 8 \\
\hline
-1 & 0.5 \\
\hline
0 & -1 \\
\hline
1 & -2.5 \\
\hline
2 & -10 \\
\hline
\end{tabular}
\][/tex]
We can write down each step of obtaining these values clearly:
1. For [tex]\( x = -2 \)[/tex]: The function [tex]\( g \)[/tex] gives us [tex]\( g(-2) = 8 \)[/tex].
2. For [tex]\( x = -1 \)[/tex]: The function [tex]\( g \)[/tex] gives us [tex]\( g(-1) = 0.5 \)[/tex].
3. For [tex]\( x = 0 \)[/tex]: The function [tex]\( g \)[/tex] gives us [tex]\( g(0) = -1 \)[/tex].
4. For [tex]\( x = 1 \)[/tex]: The function [tex]\( g \)[/tex] gives us [tex]\( g(1) = -2.5 \)[/tex].
5. For [tex]\( x = 2 \)[/tex]: The function [tex]\( g \)[/tex] gives us [tex]\( g(2) = -10 \)[/tex].
Each value of [tex]\( g(x) \)[/tex] at the respective [tex]\( x \)[/tex] values has been clearly matched from the table. The table accurately represents the function [tex]\( g \)[/tex] through its discrete points.
Now, let's put this into cohesive statements:
- When [tex]\( x = -2 \)[/tex], [tex]\( g(x) = 8 \)[/tex].
- When [tex]\( x = -1 \)[/tex], [tex]\( g(x) = 0.5 \)[/tex].
- When [tex]\( x = 0 \)[/tex], [tex]\( g(x) = -1 \)[/tex].
- When [tex]\( x = 1 \)[/tex], [tex]\( g(x) = -2.5 \)[/tex].
- When [tex]\( x = 2 \)[/tex], [tex]\( g(x) = -10 \)[/tex].
In summary, we have successfully matched each [tex]\( x \)[/tex] value in the provided table with its corresponding [tex]\( g(x) \)[/tex] value. This allows us to understand the behavior of the function [tex]\( g \)[/tex] at specific discrete points.
