\begin{tabular}{|r|r|}
\hline
[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline
-1 & 3 \\
\hline
-1 & 2 \\
\hline
0 & -4 \\
\hline
4 & 2 \\
\hline
\end{tabular}

Graph the relation shown in the table. Is the relation a function? Why or why not?

A. No; a horizontal line passes through two graphed points.
B. Yes; no vertical line passes through two graphed points.
C. Yes; no horizontal line passes through two graphed points.
D. No; a vertical line passes through two graphed points.



Answer :

To determine whether the relation shown in the table is a function, let's graph the points and examine the behavior of vertical lines passing through these points.

Here are the points given:
[tex]\[ \begin{array}{|r|r|} \hline x & y \\ \hline -1 & 3 \\ \hline -1 & 2 \\ \hline 0 & -4 \\ \hline 4 & 2 \\ \hline \end{array} \][/tex]

We can plot these points on a Cartesian plane.

1. Point (-1, 3): Located at [tex]\( x = -1 \)[/tex] and [tex]\( y = 3 \)[/tex].
2. Point (-1, 2): Located at [tex]\( x = -1 \)[/tex] and [tex]\( y = 2 \)[/tex].
3. Point (0, -4): Located at [tex]\( x = 0 \)[/tex] and [tex]\( y = -4 \)[/tex].
4. Point (4, 2): Located at [tex]\( x = 4 \)[/tex] and [tex]\( y = 2 \)[/tex].

Next, let's analyze these points:

- Vertical Line Test: For the relation to be a function, no vertical line should intersect the graph at more than one point.

Let’s now determine if any vertical line intersects more than one of these points:
- A vertical line at [tex]\( x = -1 \)[/tex] will pass through both (-1, 3) and (-1, 2).

Since the vertical line at [tex]\( x = -1 \)[/tex] intersects more than one point, the relation is not a function.

Therefore, the correct answer is:
- No; a vertical line passes through two graphed points.