To determine whether a relation is a function, we need to check if each input value (x-coordinate) is associated with only one output value (y-coordinate).
For option b, let's check if each input value has only one associated output value:
- (-5, 4) has an input value of -5, which is associated with an output value of 4.
- (4, 2) has an input value of 4, which is associated with an output value of 2.
- (8, 1) has an input value of 8, which is associated with an output value of 1.
- (-6, 5) has an input value of -6, which is associated with an output value of 5.
Based on this analysis, each input value in option b is associated with only one output value. Therefore, every relation in option b is actually a function. Thus, your answer is incorrect.
The correct answer is option c. In this relation, the input value 4 is associated with two different output values: 3 and 1. Therefore, option c is the relation that is not a function.