Name: Understanding Functions
Uploaded: 2019-07-19
Duration: 12 min 27 s
Description: A function is a machine that relates an input to an output. Functions have applications in algebra, calculus, science, etc. Watch this video.

Question

A hospital has $9$ floors above ground (including ground floor) and $3$ floors below ground. $T (n)$ gives the average number of times the elevator stops at the $n^{th}$ floor each day. Write the possible range of $T (n)$ . Justify your choice.

Accepted Answer

Given that, a hospital has $9$ floors above ground (including ground floor) and $3$ floors below ground and $T (n)$ gives the average number of times the elevator stops at the $n^{th}$ floor each day.

So, clearly, the elevator has to stops at each floor only once.

Here, Each value $n$ maps to one and only one value $T (n)$

So, by definition of a function, each element from the domain should have a unique image.

Thus, $T (n)$ is a function.

We know that, The domain of a function is the set of input values that the function can take.
The range of a function is the set of all output values that the function generates.

Therefore, Domain $= {- 3, - 2, - 1, 0, 1, 2, 3, 4, 5, 6, 7, 8}$ [As ground is considered as $0$ , so the $9$ floors above the ground are $0$ to $8$ and $3$ floors below the ground are $- 3, - 2, - 1$ ]

And Range is $T (n) \geq 0$

For example: $0 \leq T (n) < 1440$ because there are $1440$ minutes in $24$ hours and the lift will not return to a floor in less than one minute.

A hospital has $9$ floors above ground (including ground floor) and $3$ floors below ground. $T (n)$ gives the average number of times the elevator stops at the $n^{th}$ floor each day. Write the possible range of $T (n)$ . Justify your choice.

Important Questions on Are we Related? (Functional Relationships)

Learn and Prepare for any exam you want !

A hospital has 9 floors above ground (including ground floor) and 3 floors below ground. T(n) gives the average number of times the elevator stops at the nthfloor each day. Write the possible range of Tn. Justify your choice.

Important Questions on Are we Related? (Functional Relationships)

Learn and Prepare for any exam you want !

A hospital has $9$ floors above ground (including ground floor) and $3$ floors below ground. $T (n)$ gives the average number of times the elevator stops at the $n^{th}$ floor each day. Write the possible range of $T (n)$ . Justify your choice.