Question

A lumber yard sells square scraps of plywood with sides varying from 1 foot to 4 feet. Ed wants to use some of thesepieces to build storage cubes. The relationship between the length of the side of a cube and the volume of the cubeis expressed by the functionf(x) = x³where x is the length of a side of the cube. What is the range of this function in cubic feet for the domain given?

Answer 1

The range of the function f(x) = x³ for the domain of cube sides from 1 foot to 4 feet is from 1 cubic foot to 64 cubic feet.

Step-by-step explanation:

The question concerns the function f(x) = x³, which describes the volume of a cube with sides of length x.

The domain given is the side lengths ranging from 1 foot to 4 feet.

To find the range of this function, we calculate the volume for the smallest and largest possible cubes.

Using the function, for x = 1 foot, the volume is 1ft³.

For x = 4 feet, the volume is 64ft³.

Therefore, the range of possible volumes for this domain is 1ft³ to 64ft³.

Answer 2

Given that the relationshoip between the length of the cube and its volume is expressed as

`\begin{gathered} f(x)=x^3 \\ where \\ x\Rightarrow length\text{ of the cube} \\ \end{gathered}`

The range of the above function is the dependent values for which the function is real.

Given that the domain of the function is from 1 foot to 4 feet, this implies that

`\begin{gathered} f(x)=x^3 \\ when\text{ x=x1,} \\ f(1)=1^3 \\ \Rightarrow f(1)=1 \\ when\text{ x = 4} \\ f(4)=4^3 \\ \Rightarrow f(4)=64 \\ \\ \\ \\ \end{gathered}`

Hence, the range of the function in cubic feet varies from 4 to 64