Respuesta :
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 {[tex] x|0<=x<=0.75 [/tex]}
Range (d) is {[tex] y|0<=y<=9 [/tex]}
Answer:
Domain: [tex]\{t|0\leq t\leq 0.75\}[/tex],
Range: [tex]\{d|0\leq d\leq 9\}[/tex]
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.
[tex]\text{Distance}=\text{Speed}\times \text{Time}[/tex]
Since the bicycle travels at constant rate, so the distance traveled by bicycle at any time t (in minutes) would be [tex]d(t)=12t[/tex].
We know that domain of a function is set of all values of independent variable. We can see that independent variable is time (t).
[tex]45\text{ minutes}=\frac{45}{60}\text{ hours}=0.75\text{ hours}[/tex]
Since the bicycle travels for a total of 45 minutes that is 0.75 hours , so domain of our function is restricted to interval [tex]0\leq t\leq 0.75[/tex] that is [tex]\{t|0\leq t\leq 0.75\}[/tex] in set notation.
To find the upper limit of range of our given function, we will substitute [tex]t=0.75[/tex] in our function as:
[tex]d(t)=12t[/tex]
[tex]d(0.75)=12(0.75)[/tex]
[tex]d(0.75)=9[/tex]
Therefore, the range of our given function would be [tex]0\leq d\leq 9[/tex] that is [tex]\{d|0\leq d\leq 9\}[/tex] in set notation.
