Answer: R = {0kg, 59.5kg}
Explanation:
When we have a function f(x) = y.
The set of the possible values of x is called the domain of the function, and the set of the possible values of y is called the range of the function,
In this case, we have that:
the plant recycled 4.9kg the first hour, and 7.8 kg per hour after.
So this function can be written as piecewise function, with one part for the first hour, and another part for the time after the first hour.
F(x) = 4.9kg*x if 0h < x ≤ 1h
F(x) = 4.9kg + 7.8kg/h*(x -1) if x ≥ 1h
We use (x - 1) for the second part because if x = 1 h, we must have the same result in both parts of the function.
Where x is the number of hours.
And we know that the domain is (0hours, 8 hours)
Then the minimum value of y will be:
F(0h) = 4.9kg*0h = 0kg.
And the maximum value in the range will be:
F(8h) = 4.9kg + 7.8kg*7 = 59.5kg
Then the range is:
R = {0kg, 59.5kg}