Question

A box can hold no more than 16 books. The function f(b) = -b + 16 gives you the number of books you can still put in the box after b books have been put in the box.

a) f(b) is defined for b ≤ 16.
b) f(b) is defined for b ≥ 0.
c) f(b) is defined for all real values of b.
d) f(b) is undefined for all values of b.

Answer 1

The function f(b) is defined for b ≤ 16 and b ≥ 0, meaning it is defined for non-negative integers up to 16, corresponding to the number of books that can be placed into the box up to its capacity.

Step-by-step explanation:

The function f(b) = -b + 16 represents the number of books that can still be put in a box after b books have been placed inside it, with the capacity for no more than 16 books. If we are considering the domain of f(b), it should be such that the number of books already in the box (b) should be a non-negative number that is less than or equal to 16, as you cannot put a negative number of books in a box and it cannot exceed the capacity of the box. Therefore, the correct option is:

a) f(b) is defined for b ≤ 16.

b) f(b) would also be correctly defined for b ≥ 0 since you cannot have a negative number of books.

Options c) and d) do not make sense in this context because the function cannot be defined for all real values of b as the box cannot hold a negative number of books, and the function cannot be undefined for all values of b because it has a practical application within the constraints of non-negative integers up to and including 16.