Question

Which of the following represents a function?


A.
X -11 -5 -11 3
Y 15 15 21 14



B.
X -11 -5 -1 -5
Y 15 13 15 14



C.
X -11 -5 -1 -1
Y 15 13 15 14



D.
X -11 -5 -1 3
Y 15 13 21 15

Answer 1

If x-values duplicate, check if the duplicated x-values have the same value for y. If the y-values differ, then it is not a function.
Thus, if the x-values are all distinct, it is a function.

Answer 2

so this would be A b c or d ??

Answer 3

Example:
for A,
X -11 -5 -11 3
Y 15 15 21 14
there are two identical values of A (-11, 15) and (-11,21)
Since a function has to have a unique value of y for any value of x, A cannot be a function. In other words, it does not know what to return as the function value for x=-11 (15 or 21?).
Try the same way for others.
Hint: functions which do not duplicate in x would be functions.