How Tables Fail the Vertical Line Test

1 Each of the graphs below is also represented by a table. Use the vertical line test to determine whether or not each graph represents a function.

Function or Not a Function?

x	-2	-1	1	1	2
y	1	2	0	-1	1

x	-2	-1	0	1	2
y	4	1	0	1	4

x	2	1	0	1	2
y	2	-1	0	-1	-2

2 For each graph that failed the vertical line test, label the offending points with their coordinates.

3 Find the same coordinates in the table below the graph and circle or highlight them.

4 What do the tables of the non-functions have in common? What could you look for in other tables to identify whether or not they could represent a function?

5 Use the process you just described to determine whether each table below could represent a function. Circle or highlight the points that would end up on the same vertical line.

x	y
0	-2
1	-2
2	-2
3	-2
4	-2

x	y
0	-2
1	1
2	4
3	7
3	10

x	y
0	3
1	4
-1	5
2	6
-2	7

x	y
1	0
0	1
1	2
2	3
3	4

Function or Not?

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