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)

Question

Responses

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 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 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 decrease to negative infinity.

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.

Answer 1

The correct response regarding the end behavior of the volume of a sphere as the radius changes is:

As the radius increases to infinity, the volume of the sphere will increase to infinity.

This is because the volume \( V \) of a sphere is directly proportional to the cube of the radius \( r \), as indicated by the equation \( V = \frac{43}{3} \pi r^3 \). As \( r \) becomes larger and approaches infinity, \( r^3 \) also approaches infinity, leading to the conclusion that the volume \( V \) will also increase without bound.

The other options involving negative infinity are not applicable in the context of physical dimensions, as the radius of a sphere cannot be negative.