Identify whether the relation below models a proportional relationship

Yes because a propprtion is 2 numbers under each other like 12 is under 8 like a fraction form.

The relationship below does not model a proportional relationship. This is due to the fact that when you divide each domain (another word for input, or x) by its range (another word for output, or y), each result it not similar.

For example:

12 / 8 = 1.5

24 / 24 = 1

36 / 32 = 1.125

and so on.

As you can see, the rate changes throughout the table and does not stay similar. Though, it would be proportional if, for example, each x / y were equal to 1.5

see attached

step-by-step explanation:

given the function as;

write the equation replacing f(x) with y

form   and fill a table containing values of y with corresponding values of x

you can take a range for   values of x as -3≤x≤3

solving for x=-3

for x=-2

repeat the same procedure to get the values of y for the remaining ,x=-1 to x=3

plot the values of y against values   of x and obtain the following graph