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.
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.
