Question

*help requested*
*fan and medal awarded*
Part 1: Create a relation of five ordered pairs that is a function. In complete sentences explain why this relation is a function.
Part 2: Create a relation of five ordered pairs that is not a function. In complete sentences explain why this relation is not a function.

Answer 1

for the first one:

make any five ordered pairs you like
\(\{(1,2),(2,3),...\}\)
so long as the first coordinates are all distinct (no repeats) it is a function

Answer 2

for the second one, again make 5 ordered pairs, any of your choosing.
but this time, make sure there IS a repeat of the first coordinate. like for example
\[\{(1,2), (1,3),...\}\] you can fill in the rest i am sure

Answer 3

that is the only distinction between a relation that is a function, and one that is not.
if there is a repeat in the first coordinate, it is NOT a function
if there is no repeat in the first coordinate, it IS a function

Answer 4

[1,2] [2,3] [3,4] [4,5] [5, 6]
the first coordinates are all distinct (no repeats) it is a function
[1,2] [1,3] [3,4] [4,5] [5, 6]
if there is a repeat in the first coordinate, it is NOT a function
if there is no repeat in the first coordinate, it IS a function
would this be correct ?

Answer 5

yes, although if i were writing it i would replace the word "if" by "since"

Answer 6

okay thanks :)

Answer 7

[1,2] [1,3] [3,4] [4,5] [5, 6]
BECAUSE there is a repeat in the first coordinate, it is NOT a function

Answer 8

you got it