The equation V=43πr3 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)
Responses
As the radius increases to infinity, the volume of the sphere will increase to infinity.
As the radius increases to infinity, the volume of the sphere will increase to infinity.
As the radius decreases to negative infinity, the volume of the sphere will remain constant.
As the radius decreases to negative infinity, the volume of the sphere will remain constant.
As the radius decreases to negative infinity, the volume of the sphere will increase to infinity.
As the radius decreases to negative infinity, the volume of the sphere will increase to infinity.
As the radius increases to infinity, the volume of the sphere will decrease to negative infinity.
As the radius increases to infinity, the volume of the sphere will increase to infinity.
The correct answer is:
As the radius increases to infinity, the volume of the sphere will increase to infinity.
The equation V = 43πr^3 shows a cubic relationship between the volume (V) of a sphere and its radius (r). The end behavior of a cubic equation, such as this, can be determined by examining the sign of the coefficient of the highest-degree term (r^3).
In this case, the coefficient is positive (43π), which means that as the radius increases to infinity, the volume of the sphere will also increase to infinity. This can be seen by considering that as the radius becomes larger and larger, the volume of the sphere will also become larger and larger.
Therefore, the correct statement is: As the radius increases to infinity, the volume of the sphere will increase to infinity.