Question

Andrew has a fish tank in the shape of a rectangular prism, and he needs to know the volume of water necessary to fill the tank. He does not know the width of the tank, but he knows that the following graph models the volume of the tank, in cubic inches, when the tank has a width of w

what is the domain of the volume function?

A) (3, 5)

B) (0, ∞)

C) (0, 3)

D) (3, ∞)

Answer 1

The correct option is D.

Explanation:

Domain is the set of all posible

The volume of a rectangular prism is

`V=\text{Base area}* height`

where,

`\text{Base area}=length* width`

Dimensions can not be negative. So, the width and volume are always positive.

From the graph it is noticed that

In interval
`(-\infty, -5)`, width and volume is negative, so
`(-\infty, -5)` interval is not the domain.

In interval (-5,0), width is negative, so (-5,0) interval is not the domain.

In interval (0,3), volume is negative, so (0,3) interval is not the domain.

In interval
`(3,\infty)`, width and volume is negative, so
`(3,\infty)` interval is not the domain.

Therefore the correct option is D.