A floor refinishing company charges $1.87 per square foot to strip and refinish a tile floor for up to 1000 square feet. There is an additional charge of $250 for toxic waste disposal for any job which includes more than 150 square feet of tile.
A. Find the Domain and Range
Domain: The domain in this case would be the range of possible square footage for a floor refinishing job. Since the company charges up to $1.87 per square foot for up to 1000 square feet, the domain would be any value between 0 and 1000, inclusive.
Range: The range would be the cost of the floor refinishing job. It would depend on the square footage of the job and whether or not toxic waste disposal is required. So, the range would be any value that includes the cost of the job (including additional charges for toxic waste disposal), which could vary depending on the square footage.
The domain represents the possible values for the input variable, which in this case is the square footage of the tile floor. Since the company charges per square foot, the domain is all non-negative real numbers.
Domain: x ≥ 0 (where x represents the square footage of the tile floor)
The range represents the possible values for the output variable, which is the cost of the service. The cost can vary depending on the square footage of the tile floor and whether toxic waste disposal is required. However, the minimum cost would be $0 (for a floor with no square footage) and there is no maximum limit.
Range: y ≥ 0 (where y represents the cost of the service)
To find the domain and range in this scenario, we need to consider the restrictions and limitations given in the problem.
Domain:
The domain refers to the set of all possible input values for a function. In this case, the input value is the square footage of the tile floor. The problem states that the company charges $1.87 per square foot for up to 1000 square feet. Therefore, the domain is the range of possible square footage (x) such that 0 ≤ x ≤ 1000.
Domain: 0 ≤ x ≤ 1000
Range:
The range refers to the set of all possible output values for a function. In this case, the output value is the cost of the service.
The problem states that the company charges $1.87 per square foot to strip and refinish a tile floor. Additionally, there is an additional charge of $250 for toxic waste disposal for any job which includes more than 150 square feet of tile.
To calculate the cost of the service, we can use the following equation:
Cost = (Cost per square foot * Square footage) + Additional charge
For tile floors with 0 ≤ x ≤ 150 square feet, the cost would be:
Cost = (1.87 * x) + 0
For tile floors with 150 < x ≤ 1000 square feet, the cost would be:
Cost = (1.87 * x) + 250
Therefore, the range is the set of all possible values for the cost of the service:
Range: C = {(1.87 * x) + 0}, for 0 ≤ x ≤ 150
C = {(1.87 * x) + 250}, for 150 < x ≤ 1000
domain: 0 <= x <= 1000
range: 0 <= y <= 250 + 1.87 * 1000