A carpenter has 28 nails from a previous job and needs to buy more. A store has 7 boxes of nails and each box contains 100 nails. The carpenter needs to buy at least 3 boxes. The number of nails the carpenter will have after purchasing n boxes is represented by a function. f(n)=100n+28 What is the practical domain of the function?
Answers
Answer:
all integers from 3 to 7, inclusive
Step-by-step explanation:
just took the quiz
This question is based on range and domain of a function:
The domain of a function is the set of possible values for the independent variable, which in this case is n, or the number of nail boxes.
Based on the available domain values, the range is the set of possible values for the dependent variable.
The domain must be greater than 3 because the carpenter needs to buy at least 3 boxes. Since, carpenter cannot buy a fraction of a box, n must be an integer.
As the store has only 7 boxes of nails, n cannot be larger than 7.
Therefore, the domain is (B) all integers from 3 to 7, inclusive, which can be expressed symbolically as D : [ 3 , 7 ] .
The given function is: f(n)=100n+28
To find: The practical domain of the function.
For this function the total set of domain is only seven distinct numbers.
Therefore, inputting each value from the set
n = 3, 4 , 5 , 6 , 7 into the function
f (n ) = 100 n + 28 , this will give the total range as
R : 328 , 428 , 528 , 628 , 728.