Question

A bicyclist travels at a constant speed of 12 miles per hour for a total of 45 minutes. (Use set notation for the domain and range of the function that models this situation.)

Answer 1

Domain:
`\t`,

Range:
`\d`

Explanation:

We have been given that a bicyclist travels at a constant speed of 12 miles per hour for a total of 45 minutes. We are asked to write the domain and range of the function in set notation.

`\text{Distance}=\text{Speed}* \text{Time}`

Since the bicycle travels at constant rate, so the distance traveled by bicycle at any time t (in minutes) would be
`d(t)=12t`.

We know that domain of a function is set of all values of independent variable. We can see that independent variable is time (t).

`45\text{ minutes}=(45)/(60)\text{ hours}=0.75\text{ hours}`

Since the bicycle travels for a total of 45 minutes that is 0.75 hours , so domain of our function is restricted to interval
`0\leq t\leq 0.75` that is
`\0\leq t\leq 0.75\` in set notation.

To find the upper limit of range of our given function, we will substitute
`t=0.75` in our function as:

`d(t)=12t`

`d(0.75)=12(0.75)`

`d(0.75)=9`

Therefore, the range of our given function would be
`0\leq d\leq 9` that is
`\0\leq d\leq 9\` in set notation.

Answer 2

A bicyclist travels at a constant speed of 12 miles per hour for a total of 45 minutes.

We know the formula , Distance = speed * time

Speed is constant and it is 12. So it is linear

The function becomes d = 12t, x is the t is the time and d is the distance

At the starting point, t=0 and distance d=0

End point , t=45 min = 0.75 hours and distance = 12 * 0.75 = 9

So domain (t) is {
`x|0<=x<=0.75`}

Range (d) is {
`y|0<=y<=9`}