Question

Is this relation a function? If not, explain why.
(10,1) (11,6) (12,11) (13,16)(14,21)

Answer 1

The relation provided is a function because each x value is paired with exactly one y value, fulfilling the definition of a function.

Step-by-step explanation:

Based on the set of points given, namely (10,1), (11,6), (12,11), (13,16), and (14,21), the relation appears to satisfy the condition of each input (x value) being paired with exactly one output (y value). The relation provided is a function because each x value is paired with exactly one y value, fulfilling the definition of a function.

Therefore, the relation is a function. A function is defined by the relation between two variables, where each input has exactly one output. In this specific instance, no x value is repeated with a different y value, which is a fundamental criterion determining whether a relation is a function.

The dependence of y on x is seen as the y value increases consistently as x increases, which can be represented by a straight line when plotted on a graph, indicative of a linear relationship.

Answer 2

yes

Step-by-step explanation:

Yes, the given set of ordered pairs {(10, 1), (11, 6), (12, 11), (13, 16), (14, 21)} represents a function. In a function, each input (x-value) is associated with exactly one output (y-value). In this case, for each x-value, there is a unique y-value. Therefore, it satisfies the definition of a function.