A long distance phone service charges $0.30 for the first 10 minutes and $0.05 for each additional minute or fraction thereof. U
se the greatest integer function to write the cost C of a call in terms of time t (in minutes). Sketch the graph of this function and discuss its continuity.
1 answer:
Answer: Our Cost function is discontinuous at every integer after x>10.
Step-by-step explanation:
Since we have given that
For the first 10 minutes , the service charges = $0.30
Let the number of additional minute be 't'.
Amount charge for each additional minute = $0.05
Using the greatest integer function:
So, Cost C of a call in terms of time 't' minutes would be
As we know that Greatest integer is discontinuous at every integer.
So, our Cost function is discontinuous at every integer after x>10.
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Answer:
C.
Step-by-step explanation:
Let's find the inverse of each of the given options.
Option A:
To find , replace 'x' with 'y' and 'y' with 'x'. This gives,
Rewrite in terms of 'y'. This gives,
The given function
So, option A is incorrect.
Option B:
To find , replace 'x' with 'y' and 'y' with 'x'. This gives,
Rewrite in terms of 'y'. This gives,
The given function
So, option B is incorrect.
Option C:
To find , replace 'x' with 'y' and 'y' with 'x'. This gives,
Rewrite in terms of 'y'. This gives,
The given function
So, option C is correct.
Option D:
To find , replace 'x' with 'y' and 'y' with 'x'. This gives,
Rewrite in terms of 'y'. This gives,
The given function
So, option D is incorrect.
Therefore, only option C is correct.