For a given function y = f(x), the domain is the set of the possible values of x, and the range is the set of the possible values of y.
In this problem, the domain is: 0h ≤ t ≤ 7.5h
And the range is: 0mi ≤ D(t) ≤ 15mi
Here we do know that Augustine walks 15 miles, at a speed of 2mi/h.
Remember the equation:
distance = speed*time
Then the function will be:
D(t) = (2mi/h)*t
Where t is the time in hours.
The easier thing to find is the range. We know that she walks 15 miles, then the maximum of the range will be 15 miles (and the minimum is 0 miles, the initial amount).
Then the range is:
0mi ≤ D(t) ≤ 15mi
To find the domain we need to find the value of t such that the distance is equal to the maximum in the range, so we need to solve:
D(t) = 15mi = (2mi/h)*t
(15mi )/(2mi/h) = t = 7.5 h
This means that the maximum of the domain is 7.5 hours (and the minimum is 0 hours) then the domain is:
0h ≤ t ≤ 7.5h
If you want to learn more, you can read:
https://brainly.com/question/1632425
