The comparison between the mathematical range and the reasonable range is:
Mathematical Range: (y ∈ ℝ, y ≠ 0)
Reasonable Range: (y ∈ ℝ, y > 0)
Mathematical range and reasonable range for the function
The mathematical range and reasonable range for the function
f(x) = 5,000/x are as follows:
Mathematical Range: (y ∈ ℝ, y ≠ 0)
The mathematical range represents all possible values of y that the function can output. In this case, y can take any real number value except for 0 since dividing by zero is undefined.
Reasonable Range: (y ∈ ℝ, y > 0)
The reasonable range represents the values of y that make sense in the given context or problem.
In this case, since we are dealing with the number of oranges, the reasonable range would be y greater than zero. It doesn't make sense to have a negative number or zero as the average number of oranges produced by x number of trees.
Therefore, the comparison between the mathematical range and the reasonable range is:
Mathematical Range: (y ∈ ℝ, y ≠ 0)
Reasonable Range: (y ∈ ℝ, y > 0)
So, the correct answer is:
mathematical: (y ∈ ℝ, y ≠ 0) reasonable: (y ∈ ℝ, y > 0)