Question

The following equation represents the volume of a rectangular prism with a width of winches:V= 2w^3 - 7w^2 +3wa Graph the polynomial on a graphing calculator or an online graphing application. Whatare the 2-intercepts? What do these mean in terms of the situation?b What are the domain and range in terms of the situation? Justify your answers.

Answer 1

(a) The graph of the function

`V=2w^3-7w^2+3w`

is shown below

From the graph, the two intercepts considered are (0.5, 0) and (3, 0)

They indicate that the width of prism would be 0.5 or 3.0 when the volume of the prism is 0.

(b) The domain are the values for which the x-values, in this case width values are valid. These are points on the graph, where the volume (y-values) would be positive for width (x-values). From the graph, these are x-vaues of 0 to 0.5 or 3 to infinity.

So in interval notation, the domain is

`(0,0.5)\cup(3,\infty)`

The range are the values for which the y-values, in this case volume values are valid. Since volume of a prism cannot be negative, so the range is a set of all positive y values

Hence the range is

`y>0`