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In a factory, a certain machine needs 10 min to warm up. it takes 15 min for the machine to run a cycle. the machine can operate for as long as 6 h per day including warm up time. Draw a graph showing the total time the machine operates during 1 day as a function of the number of cycles it runs.

-What domain and range are reasonable?
-Is the function a linear function?

User SRy
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1 Answer

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Answer:


y =(1)/(6) + 0.25x


0 \leq x \leq23.33



0 \leq y \leq 6

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:



y =(1)/(6) + 0.25x

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:



x\geq 0 (because you can not perform less than zero cycles a day)



x \leq23.33. Because the machine can not exceed 6 hours per day, then it can not do more than 23.33 cycles.


So:



0 \leq x \leq23.33


The range of the function is:



y \geq 0 (because you can not work less than 0 hours a day)



y \leq 6 (because the machine can not work more than 6 hours a day)


So



0 \leq y \leq 6

In a factory, a certain machine needs 10 min to warm up. it takes 15 min for the machine-example-1
User Eric Cousineau
by
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