Question

Cartons of eggs are sold 4 dollars per dozen. They can be purchased by the 1 dozen, 1.5 dozen, 3 dozen, or 12 dozen. The cost in dollars of the eggs is a function of the number of dozen of eggs purchased. What are the domain and the range

Answer 1

To determine the domain and range of the cost function for cartons of eggs sold at 4 dollars per dozen, let's first define the variables involved.

1. **Domain**: The domain refers to the possible input values of the function, which in this case corresponds to the number of dozens of eggs that can be purchased. The eggs can be purchased in increments of dozen, given the options available:

- 1 dozen
- 1.5 dozen
- 3 dozen
- 12 dozen

Thus, the domain can be expressed as the discrete set of values: \(\{1, 1.5, 3, 12\}\).

2. **Range**: The range refers to the possible output values of the function, which in this case corresponds to the cost of the eggs based on the number of dozens purchased. The cost can be calculated by multiplying the number of dozens by the price per dozen ($4).

- For 1 dozen: \(1 \times 4 = 4\) dollars
- For 1.5 dozen: \(1.5 \times 4 = 6\) dollars
- For 3 dozen: \(3 \times 4 = 12\) dollars
- For 12 dozen: \(12 \times 4 = 48\) dollars

Therefore, the range of the function is: \(\{4, 6, 12, 48\}\).

In conclusion, the domain and range are as follows:

- **Domain**: \(\{1, 1.5, 3, 12\}\)
- **Range**: \(\{4, 6, 12, 48\}\)