Question

Noah finds an expression for V(x) that gives the volume of an open-top box in cubic inches in terms of the length x in inches of the cutout squares used to make it. This is the graph Noah gets if he allows x to take on any value between -1 and 5.What is a reasonable domain for V in this context?

Answer 1

We are given the graph of a function V(x) that gives the volume of an open-top cube with x being the length in inches of the squares used to make the cube.

We are asked to identify its reasonable domain.

To do this, we will have to inspect the given graph and identify where V(x) would make sense. Remember that V(x) stands for the volume of a cube. Therefore, it can only have values that are positive.

Here, we see that the graph is above the x-axis when 0 < x < 2.5 and 3.5 < x < 5. When the graph is above the x-axis, then V(x) is positive.

Therefore, the reasonable domain would be (0, 2.5) U (3.5, 5).