Question

Consider a rectangle with width of x units and an area of 10 square units. The length l of the rectangle can be modeled by the function f (x) = StartFraction 10 Over x EndFraction.

Answer 1

third graph

Explanation:

Answer 2

When we have a rectangle of width W and length L, the area of this rectangle can be calculated as:

A = W*L

In this case we have:

W = x

L = 10/x.

Then the area of the rectangle will be:

A = W*L = x*(10/x) = 10

So the value of x cancels in the equation, which means that we can not find the value of x.

Now, as L = 10/x we can find some restrictions:

if x = 0, we would have L = 10/0

So we can not have x = 0.

And as W = x, this represents a positive measure, we also have that x can not be a negative number.

So the relation:

W = x

L = 10/x

Gives us all the possible combinations of width and length such that the area of the rectangle is exactly 10 square units.