Question

which graph represents the same relation as the table below? \

$$\begin{tabular}{|c|c|} \\hline \\textbf{x} & \\textbf{f(x)} \\\\ \\hline -2 & 5 \\\\ \\hline 0 & 1 \\\\ \\hline 1 & -1 \\\\ \\hline 2 & -3 \\\\ \\hline \\end{tabular}$$

(graph with coordinate plane and points as shown)

Explanation:

Step1: Identify Table Points

The table has points: $(-2, 5)$, $(0, 1)$, $(1, -1)$, $(2, -3)$.

Step2: Analyze Given Graph

Check if the graph has these points. The given graph shows points at $(-2, 5)$, $(-1, 1)$, $(0, -1)$ – which don't match all table points. Wait, maybe the full graph (not fully shown) should have points matching $x$ and $f(x)$ from the table. Let's list each table point's coordinates:

• For $x=-2$, $f(x)=5$: point $(-2, 5)$.
• For $x=0$, $f(x)=1$: point $(0, 1)$.
• For $x=1$, $f(x)=-1$: point $(1, -1)$.
• For $x=2$, $f(x)=-3$: point $(2, -3)$.

We need to find the graph with these four points. Since the provided graph in the image has some points, but likely the correct graph (not fully shown here) will plot $(-2,5)$, $(0,1)$, $(1,-1)$, $(2,-3)$. Assuming the options (even if partially shown) should have these points. Wait, maybe the user's graph options (though partially visible) – but the key is to match the table's $(x, f(x))$ to the graph's plotted points.

Answer:

(Assuming the correct graph has points $(-2,5)$, $(0,1)$, $(1,-1)$, $(2,-3)$ – likely the graph (not fully shown here) that includes these coordinates. If among options, the one with these four points. But based on the table, the correct graph should have points at $x=-2,y=5$; $x=0,y=1$; $x=1,y=-1$; $x=2,y=-3$.)