Question

which relation is not a function? a) x-y mapping diagram with 1→2, 3→4, 5→4, 7→8 b) x-y mapping diagram with 2→6, 8→6, 9→6 c) x-y mapping diagram with 5,6,7 mapping to 1,2,3 (partial view)

Explanation:

Step1: Recall the definition of a function

A relation is a function if each input (x - value) has exactly one output (y - value). In other words, no x - value is mapped to more than one y - value.

Step2: Analyze option a

In option a, the x - values are 1, 3, 5, 7. Each of these x - values is mapped to only one y - value. 1 is mapped to 2 and 4? Wait, no, looking at the diagram: 1 is mapped to 2 and 4? Wait, no, maybe I misread. Wait, the first oval (x) has 1, 3, 5, 7. The second oval (y) has 2, 4, 8. Wait, 1 is connected to 2 and 4? Wait, no, maybe the diagram is: 1→2, 3→4, 5→4, 7→8? Wait, no, the original diagram: 1 is connected to 2 and 4? Wait, no, maybe I made a mistake. Wait, let's re - analyze.

Wait, the key is: for a function, each x must have at most one y. Let's check option c (assuming the third option is c). In option c, the x - value 6 is mapped to more than one y - value (since there are multiple arrows from 6 to different y - values). Wait, let's look at the options again.

Option a: x - values 1, 3, 5, 7. Each x has one y (1→2, 3→4, 5→4, 7→8? Wait, 3 and 5 both map to 4, which is allowed in a function (multiple x can map to the same y, but not the same x to multiple y).

Option b: x - values 2, 8, 9. Each x maps to 6. So 2→6, 8→6, 9→6. This is a function (multiple x to same y is okay).

Option c: The x - value 6 has multiple arrows to different y - values (like 1, 2, 3 etc.). So 6 is mapped to more than one y - value, which violates the definition of a function. So the relation that is not a function is option c.

Answer:

c (the third option, with the x - value 6 having multiple y - mappings)