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

Answer:

Domain: $\{t|0\leq t\leq 0.75\}$,

Range: $\{d|0\leq d\leq 9\}$

Step-by-step 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.

$\text{Distance}=\text{Speed}\times \text{Time}$

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).

$45\text{ minutes}=\frac{45}{60}\text{ hours}=0.75\text{ hours}$

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 $\{t|0\leq t\leq 0.75\}$ 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 $\{d|0\leq d\leq 9\}$ 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 {$x|0$}

Range (d) is {$y|0$}