Question

hannah approximates the area of circles using the equation ( a = 3r^{2} ) and records areas of circles with different radius lengths in a table. answer parts a and b.

radius (in.)	2	4	6	8	10

a. graph the ordered pairs from the table. choose the correct graph below.

b. is the relation a function? explain your answer.

the relation (square)a function because (square) corresponds (square) one (square)

Explanation:

Step1: Identify ordered pairs

The ordered pairs from the table are \((2,12)\), \((4,48)\), \((6,108)\), \((8,192)\), \((10,300)\).

Step2: Analyze graph B

In graph B, when \(r = 2\), \(y=12\); when \(r = 4\), \(y = 48\); when \(r=6\), \(y = 108\); when \(r = 8\), \(y=192\); when \(r = 10\), \(y = 300\).

Step3: Check function definition

A relation is a function if for each input (radius \(r\)) there is exactly one output (area \(A\)). In the given table, for each value of the radius, there is a unique value of the area.

Answer:

a. Graph B is correct.
b. The relation is a function because each input (radius) corresponds to exactly one output (area).