Question

Consider the two groups listed below. Which statement describes the sets?
the length of a swimming pool
the liquid volume of the pool

The relation (length, volume) is a function, but the relation (volume, length) is not.
The relation (volume, length) is a function, but the relation (length, volume) is not.
Both the relation (length, volume) and the relation (volume, length) are functions.
Neither the relation (length, volume) nor the relation (volume, length) is a function.

@mathstudent55

Answer 1

First, remember that in a function, no two points can have the same x-coordinate.
Each x-coordinate can only occur once.

Answer 2

If the pool you are dealing with is a rectangular prism, then its volume is the product of its length, its width , and its height.

\(\Large V = lwh\)

Answer 3

You can find many values of the length that will give you the same volume.
For example:

L = 20 ft
W = 10 ft
H = 8 ft
The volume is 1600 ft^3

Now let
L = 20 ft
W = 8 ft
H = 8 ft
The volume is now 1280 ft^3

You see that for the same value of the length, 20 ft, you ended up with two different volumes.
That means that the relation (length, volume) is not a function.

Answer 4

Now try to see if you can come up with an example of the relation (volume, length) in which the same volume gives two different lengths.

Answer 5

hmm still kind of confusing. So it would be: "The relation (volume, length) is a function, but the relation (length, volume) is not?"

Answer 6

Look at these examples of the relation (volume, length):

1:
volume = 2000 ft^3
length = 40 ft
width = 10 ft
height = 5 ft

2:
volume = 2000 ft^3
length = 20 ft
width = 10 ft
height = 10 ft

You see that we can come up with a value of the volume that will be matched to several different lengths. That means the relation (volume, length) is also not a function.