Answer:
[tex]y =\frac{1}{6} + 0.25x[/tex]
[tex]0 \leq x \leq23.33[/tex]
[tex]0 \leq y \leq 6[/tex]
Step-by-step explanation:
The machine always takes 10 minutes (or 1/6 hours) to warm up and performs each cycle in 15 minutes, or 0.25 hours.
The maximum amount of daily hours that the machine can work is 6 hours.
Therefore we can represent this situation by means of an equation of the form:
[tex]y =\frac{1}{6} + 0.25x[/tex]
Where
y = daily amount of hours the machine works.
x = number of daily cycles performed.
This equation is a linear function. Because it has the form y = ax where a is a real number
The graph of this equation is shown in the attached image, where the gray shaded area represents the domain of the function.
The domain of the function is:
[tex]x\geq 0[/tex] (because you can not perform less than zero cycles a day)
[tex]x \leq23.33[/tex]. Because the machine can not exceed 6 hours per day, then it can not do more than 23.33 cycles.
So:
[tex]0 \leq x \leq23.33[/tex]
The range of the function is:
[tex]y \geq 0[/tex] (because you can not work less than 0 hours a day)
[tex]y \leq 6[/tex] (because the machine can not work more than 6 hours a day)
So
[tex]0 \leq y \leq 6[/tex]
