Which of the following relations is a function?
IT's only the FIRST COORDINATES that determine this.
Look at ALL FIRST COORDINATES. If any FIRST COORDINATE is used twice, then
the relation is NOT a function. It doesn't matter at all about the SECOND
coordinates. The SECOND coordinates can even be ALL the SAME.
Or plot the graph. If any point is directly above or below any other point,
the relation is NOT a function. See the vertical line (in green)? If any
vertical line passes through two points of the relation, the relation is NOT
a function. So this is NOT a function.
This is the VERTICAL LINE test.
A.
(2, 0), (-5, 3), (9, 1), (-5, 5)
The FIRST coordinates in the ordered pairs are 2, -5, 9, and -5.
Two of the FIRST coordinates are the SAME, -5. So this relation is
NOT a function.
Or plot the graph:
See the green vertical line at -5? It passes through two points, one above
the other, so it is NOT a function. It DOES NOT pass the VERTICAL LINE TEST.
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B.
(2, 4), (-5, 2), (9, 1), (-7, 2)
The FIRST coordinates in the ordered pairs are 2, -5, 9, and -7.
NO two of the FIRST coordinates are the SAME, -5. So this relation IS a
function. It PASSES the VERTICAL LINE test.
Or plot the graph:
No vertical line can be drawn which passes through two points, no point is
above or below any other point, so it IS a function. It PASSES the VERTICAL
LINE TEST.
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C.
(2, 4), (-5, 6), (2, 3), (-7, 2)
The FIRST coordinates in the ordered pairs are 2, -5, 2, and -7.
Two of the FIRST coordinates are the SAME, 2. So this relation is
NOT a function.
Or plot the graph:
See the green vertical line at 2? It passes through two points, one above
the other, so it is NOT a function. It DOES NOT pass the VERTICAL LINE
TEST.
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D.
(9, 1), (-5, 4), (2, 1), (9, 2)
The FIRST coordinates in the ordered pairs are 9, -5, 2, and 9.
Two of the FIRST coor.dinates are the SAME, 9. So this relation is
NOT a function.
Or plot the graph:
See the green vertical line at 9? It passes through two points, one above
the other, so it is NOT a function. IT DOES NOT PASS the VERTICAL LINE
test.
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Edwin