The radius of the circle is half of the diameter. Therefore, if the diameter is 2 units, then the radius is 1 unit. If the diameter is 6 units, the radius will be 3 units. The graph that represents the relationship between radius and diameter is Graph B.
The circumference of the circle can be solved by multiplying the diameter and the value of pi. Therefore, this is a linear function. If the diameter is 4 units, the circumference is approximately 12.57 units. If the diameter is 6 units, the circumference is approximately 18.85 units. The graph that best represents the relationship between diameter and circumference is Graph C.
Lastly, the area of the circle with respect to the diameter is a quadratic function due to the nature of the formula that is A = πr². The graph of a quadratic function is parabolic in nature. Therefore, the graph that best represents the relationship between diameter and area is Graph A.
To summarize, the vertical axis for each graph is:
Graph A → Area
Graph B → Radius
Graph C → Circumference