The equation V=43πr^3 represents the relationship between the volume of a sphere and its radius. What does the end behavior tell you about the relationship between the volume of the sphere and its radius?(1 point)
1. As the radius increases to infinity, the volume of the sphere will decrease to negative infinity.
2. As the radius increases to infinity, the volume of the sphere will increase to infinity.
3. As the radius decreases to negative infinity, the volume of the sphere will remain constant.
4. As the radius decreases to negative infinity, the volume of the sphere will increase to infinity.
2. As the radius increases to infinity, the volume of the sphere will increase to infinity.
2. As the radius increases to infinity, the volume of the sphere will increase to infinity.
To determine the end behavior of the relationship between the volume of a sphere and its radius, we can examine the equation V = 43πr^3.
In this equation, the volume of the sphere is represented by V, and the radius is represented by r. The coefficient 43π indicates the relationship between the volume and the radius.
The highest degree of r in the equation is 3, which means that the end behavior of the equation will be determined by the sign of the coefficient of the highest degree term.
In this case, the coefficient is positive (43π), which means that as the radius increases without bound, the volume will also increase without bound. Therefore, the correct answer is:
2. As the radius increases to infinity, the volume of the sphere will increase to infinity.