91Ó°ÊÓ

The domain of a function includes all the possible input values for the independent variable. In our exercise, the independent variable is the number of cigarette waste cans ordered, represented by \( x \). Since the problem specifies that orders can range from 4 to 11 cans, the domain consists of the integers 4 through 11.
To express this using roster notation, we list all these values in a set: \(\text{Domain} = \{ 4, 5, 6, 7, 8, 9, 10, 11 \}\).
This means that only these specific values are allowed inputs for the function representing the number of cigarette waste cans ordered.

The range includes all possible output values of the dependent variable. In this exercise, the dependent variable is the cost of the order, represented by \( C(x) \).
We calculate the cost using the formula \( C(x) = 61.50 \times x \), for every value in the domain:
\(\begin{align*} C(4) &= 61.50 \times 4 = 246, \ C(5) &= 61.50 \times 5 = 307.50, \ C(6) &= 61.50 \times 6 = 369, \ C(7) &= 61.50 \times 7 = 430.50, \ C(8) &= 61.50 \times 8 = 492, \ C(9) &= 61.50 \times 9 = 553.50, \ C(10) &= 61.50 \times 10 = 615, \ C(11) &= 61.50 \times 11 = 676.50 \ \end{align*}\)
Expressing this in roster notation, we get: \(\text{Range} = \{246, 307.50, 369, 430.50, 492, 553.50, 615, 676.50\}\).
This shows all the possible values for the cost depending on the number of cans ordered.

A cost function helps us understand the relationship between the number of items ordered and the total cost. In our problem, the cost function is given by \(C(x) = 61.50 \times x\), where \(C(x)\) is the total cost and \(x\) is the number of cigarette waste cans ordered.
Here are the key components in this function:

• The coefficient 61.50 represents the cost per single can.
• The variable \( x \) represents the quantity of waste cans ordered.

By using this function, you can easily calculate the total cost for any quantity of cans within the domain. For example, if five cans are ordered, the total cost would be \(C(5) = 61.50 \times 5 = 307.50\). This straightforward relationship helps in budgeting and planning for any number of cans you may need within the given range.