Final answer:
To determine which relation is not a function, we need to check if any x-values are repeated with different y-values. Option (A), (B), and (C) are not functions, while option (D) is a function.
Step-by-step explanation:
A relation is a function if for every input, there is exactly one output. In other words, each x-value in the relation should have a unique y-value. We can determine if a relation is a function by checking if any x-values are repeated with different y-values.
Let's analyze the given options:
(A) (1,9) (2,7) (2,5) (3, 3) (4, 1) - This relation is not a function because the x-value 2 is repeated with different y-values 7 and 5.
(B) (-3,5) (-4,5) (-5,5) (-6,5) (-7,5) - This relation is not a function because the y-value 5 is repeated with different x-values -3, -4, -5, -6, and -7.
(C) (10, 20) (20, 40) (20, 50) (30, 60) - This relation is not a function because the x-value 20 is repeated with different y-values 40 and 50.
(D) (1, 0.5) (2, 1) (4, 3) (5, 1.5) (6, 2) - This relation is a function as each x-value has a unique y-value.
Therefore, option (A), (B), and (C) are not functions, while option (D) is a function.