Which relation is a function? {(5, 0), (0, –8), (5, –5)} {(5, 0), (0, 5), (–5, –5)} {5, 0, –8, –5} {(5, 0), (–8, –5), (–8, 5), (–5, –8)}

The third option is a function

Step-by-step explanation:

A function is a relation in which every x value is paired with exactly one y value, meaning that x values cannot repeat within a relation. The 1st and 4th options have repeating X's, and the 2nd option does not have ordered pairs, only integers.

The third option is a function

hope it helped ;)

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

cross multiplying, we get :

⇒ (3) × (5) = (9) × (x)

⇒ 15 = 9x