Final answer:
The given relation is a function because each x is paired with exactly one y. The function is non-linear because the differences between the y values are not constant.
Step-by-step explanation:
To determine whether the relation is a function, we can use the definition of a function, which states that each input x should be associated with exactly one output y. By examining the given values for x (0, 2, 4, 6) and y (-8, -3, 3, 7), we see that each x value is paired with a unique y value, which confirms that the relation is indeed a function.
To ascertain whether the function is linear or non-linear, we plot the points on a graph and observe whether they lie in a straight line. A linear function would have a constant rate of change, meaning the differences between the y values would be consistent as x increases uniformly. Here, the gaps between the y values are (-8 to -3 is 5, -3 to 3 is 6, and 3 to 7 is 4). Since these differences are not constant, the relation is non-linear.