Answer:
75 miles/min
Explanation:
This is an example of a piecewise function.
A piecewise function is a function defined by two or more expressions, where each expression is associated with a unique interval of the function's domain.
In this function, the x-axis refers to time(t) and y axis to distance(d). So we can represent this function as d = f(t)
The rate of change of the given function (the slope) is different for different intervals. We can see 3 different intervals at where the slopes are different:
0 ≤ t ≤ 2 when d goes from 0 to 30 (rate of change = 30/2 = 15)
2 ≤ t ≤ 3 when d goes from 30 to 90 (rate of change = 60/1 = 60)
3 ≤ x ≤ 4 when goes from 90 to 300 (rate of change = 210/1 = 210)
For a piecewise function f(x) , the average rate of change between x1 and x2
f(x2) - f(x1)/(x2-x1)
Here we are using t for x-axis and d for y-axis
The given interval is [0,4]
Therefore t2= 4 and t1 = 0
At t2= 4 min, f(t2) = f(4) = d2= 300 miles
At t1 = 0 min f(t1) = f(0) = d1 = 0 miles
So average rate of change in the interval [0, 4]
= (300-0)(4-0)
= 300/4 =
75 miles/min