How can you determine whether the relationship between side length and area is a function?

If it is a function, say whether it is linear or non linear function ?

The correct answer is: a linear function

Step by step solution:
Let us denote the length by x.
Let us denote the area by y.
From the table, we can observe that there is a different and unique value of y for every x.
This gives that the given relationship is a function.
Next, we draw the graph of the function to check its linearity.
We construct the following table

x	0	1	2	3	4	5
y	0	1	4	9	16	25

We plot the above points in the following graph.

Clearly, the graph is not a straight line. Hence the given relationship between length and area is not a linear function.

There are other ways to determine whether a function is linear or not, like, checking if the slope is equal between each of the points or if the equation can be written in the form of y = ax + b, where a and b are constants.