six graphs are shown below. click on the tabs to see them.\ngraph 1 graph 2 graph 3 graph 4 graph 5 graph…

six graphs are shown below. click on the tabs to see them.\ngraph 1 graph 2 graph 3 graph 4 graph 5 graph 6\ngraph 1 image: a coordinate plane with several points plotted\ncheck the box corresponding to each graph that represents a function.\n□ graph 1 □ graph 2 □ graph 3 □ graph 4 □ graph 5 □ graph 6 □ none of the graphs

six graphs are shown below. click on the tabs to see them.\ngraph 1 graph 2 graph 3 graph 4 graph 5 graph 6\ngraph 1 image: a coordinate plane with several points plotted\ncheck the box corresponding to each graph that represents a function.\n□ graph 1 □ graph 2 □ graph 3 □ graph 4 □ graph 5 □ graph 6 □ none of the graphs

Answer

To determine if a graph represents a function, we use the vertical line test: a graph is a function if no vertical line intersects it more than once.

Analyzing Graph 1:

Looking at the points in Graph 1, we check for repeated ( x )-values (since a vertical line at a specific ( x )-value should only hit one point). The ( x )-coordinates of the points are ( -4 ), ( -3 ) (wait, no—let’s list the coordinates:

  • ( (-4, 1) ) (assuming the grid: ( x=-4 ), ( y=1 ))
  • ( (0, 3) ) ( ( x=0 ), ( y=3 ))
  • ( (1, 5) ) ( ( x=1 ), ( y=5 ))
  • ( (5, 0) ) ( ( x=5 ), ( y=0 ))
  • ( (-3, -5) ) ( ( x=-3 ), ( y=-5 ))
  • ( (-1, -5) ) ( ( x=-1 ), ( y=-5 ))

Wait, ( x=-3 ) and ( x=-1 ) each have one point, ( x=-4 ), ( x=0 ), ( x=1 ), ( x=5 ) each have one point. Wait, no—wait, the two points at the bottom: ( x=-3 ) (maybe ( x=-3 )) and ( x=-1 )? Wait, no, looking at the grid: the bottom two points—let’s check their ( x )-coordinates. Suppose the left bottom point is at ( x=-3 ), ( y=-5 ), and the right bottom point is at ( x=-1 ), ( y=-5 ). So each ( x )-value has only one ( y )-value. Wait, but wait—wait, the vertical line test: for any ( x ), is there only one ( y )? Let’s check ( x=0 ): only one point ( ( 0, 3 ) and ( 0, 5 )? Wait, no—wait the graph: there are two points on the ( y )-axis? Wait, the original graph: “Graph 1” has a point at ( (0, 3) ) (since ( y=3 ) is between 2 and 4, maybe ( y=3 )) and a point at ( (0, 5) )? Wait, no, the user’s graph: “Graph 1” has two points on the ( y )-axis ( ( x=0 )): one at ( y=3 ) (or ( y=3 )) and one at ( y=5 ) (above ( y=4 ))? Wait, no—let me re-examine.

Wait, the graph shows:

  • A point at ( x=-4 ), ( y=1 ) (approx)
  • A point at ( x=0 ), ( y=3 ) (middle vertical line, ( y=3 ))
  • A point at ( x=0 ), ( y=5 ) (middle vertical line, ( y=5 ))
  • A point at ( x=5 ), ( y=0 )
  • A point at ( x=-3 ), ( y=-5 )
  • A point at ( x=-1 ), ( y=-5 )

Ah! Here’s the key: at ( x=0 ), there are two points ( ( (0, 3) ) and ( (0, 5) ) ). So a vertical line at ( x=0 ) would intersect the graph twice. Therefore, Graph 1 fails the vertical line test and is not a function.

But wait—since we only have Graph 1 visible, but the problem has six graphs. However, the user’s question is to check which graphs represent functions. Since only Graph 1 is shown, but we need to infer. Wait, no—maybe the original problem (but the user provided Graph 1). Wait, perhaps the user made a mistake, but assuming Graph 1: since it has two points with the same ( x )-value ( ( x=0 ) ), it is not a function. But if other graphs (not shown) pass the vertical line test, but since we only have Graph 1, let’s proceed.

But wait—maybe I misread. Let’s re-express:

To determine if a graph is a function, use the vertical line test: no vertical line intersects the graph more than once.

For Graph 1:

  • Check ( x=0 ): two points (different ( y )-values). Thus, vertical line ( x=0 ) intersects twice. So Graph 1 is not a function.

But since the problem has six graphs, but only Graph 1 is shown, we can’t analyze the others. However, the user’s question is to check the box for each graph that is a function. Since Graph 1 fails the vertical line test (two points on ( x=0 )), Graph 1 is not a function.

But wait—maybe the user intended to ask about Graph 1. Let’s confirm:

If a graph has two points with the same ( x )-coordinate (different ( y )-coordinates), it is not a function. In Graph 1, there are two points at ( x=0 ) (different ( y )-values), so it fails the vertical line test. Thus, Graph 1 is not a function.

But since the problem has multiple graphs, and we can only see Graph 1, we can’t answer fully. However, assuming the question is about Graph 1:

Brief Explanations:

To determine if a graph represents a function, use the vertical line test: a graph is a function if no vertical line intersects it more than once. For Graph 1, there are two points with ( x = 0 ) (different ( y )-values), so a vertical line at ( x = 0 ) intersects the graph twice. Thus, Graph 1 fails the vertical line test and is not a function.

Answer:

Graph 1: (\boldsymbol{\square}) (unchecked, since it is not a function)
(Note: For other graphs, we need to analyze them similarly, but only Graph 1 is visible here.)