Answer:
The domain of the function is [tex]Dom \{y\} = [0\,min, 2\,min][/tex].
Step-by-step explanation:
We understand that the watering can is filled at a constant rate, that is:
[tex]y =k\cdot x[/tex]
Where:
[tex]x[/tex] - Filling time, measured in minutes.
[tex]y[/tex] - Watering can volume occupied by water, measured in gallons.
[tex]k[/tex] - Filling rate, measured in gallons per minute.
If we know that [tex]k = 0.75\,\frac{gal}{min}[/tex] and [tex]y = 1.5\,gal[/tex], the final filling time is:
[tex]x = \frac{y}{k}[/tex]
[tex]x = \frac{1.5\,gal}{0.75\,\frac{gal}{min} }[/tex]
[tex]x = 2\,min[/tex]
The domain of the function corresponds to the set of real numbers between zero and final filling time. That is to say:
[tex]Dom \{y\} = [0\,min, 2\,min][/tex]
