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?
To determine the end behavior of a function, we need to examine what happens to the function as the input (in this case, the radius, denoted by 'r') approaches positive or negative infinity.
In the given equation V = 43πr^3, we can observe that as the radius, 'r', increases or decreases towards positive or negative infinity, the volume, 'V', will also increase or decrease towards positive or negative infinity, respectively.
So, the end behavior of the relationship between the volume of the sphere and its radius indicates that as the radius of the sphere becomes larger or smaller without bound, the volume of the sphere also becomes larger or smaller without bound, respectively.
The equation V = 43πr^3 is a cubic equation, where the volume (V) of the sphere is directly proportional to the cube of its radius (r^3).
Since the exponent of r is 3, the end behavior of this equation tells us that as the radius of the sphere increases or decreases, the volume will increase or decrease even more dramatically. This means that the volume of the sphere increases at a much faster rate than its radius.