Ann's ride , a piecewise function
Ann went on a 10 hour bicycle trip. The table shows selected points on the graph.
t-0-1-4-7-10
d (t)- 0-3-5-5-10.
Write a function d(t) for her total distance traveled in miles in terms of the time in hours. Please help!
idk breh
To write a piecewise function, we need to look at the given points on the graph and identify the different intervals where the function behaves differently.
From the given table, we have the following points:
t - 0-1-4-7-10
d(t) - 0-3-5-5-10
Looking at the points, we can see that the function has two distinct intervals:
1. From t = 0 to t = 7: The distance traveled is increasing, as the values of d(t) increase from 0 to 5. We can represent this interval with a linear function.
2. From t = 7 to t = 10: The distance remains constant at d(t) = 5. We can represent this interval with a constant function.
Let's write the piecewise function for the total distance traveled (d(t)) in terms of time (t):
For t < 7:
d(t) = mt + b
To find the values of m and b, we can use the first two points (0, 0) and (1, 3).
Using the formula for slope (m):
m = (change in d)/(change in t) = (3 - 0)/(1 - 0) = 3/1 = 3
Using the point-slope form of a linear equation:
y - y1 = m(x - x1) where (x1, y1) = (0, 0)
y - 0 = 3(x - 0)
y = 3x
Thus, for t < 7:
d(t) = 3t
For t >= 7:
d(t) = 5
Combining these two intervals, we can write the piecewise function d(t) as:
d(t) =
3t if 0 <= t < 7
5 if 7 <= t <= 10
Therefore, the function d(t) for her total distance traveled in miles in terms of the time in hours is:
d(t) = 3t for 0 <= t < 7
d(t) = 5 for 7 <= t <= 10