Question

You have 3 quarts of paint to paint the trim in your house. A quart of paint covers 100 ft? The function Alg)=100q represents the area A(g), in square feet, that q quarts of paint cover. What domain and range are reasonable for the function?

Answer 1

The domain is 0 ≤ q ≤ 3 and the range is 0 ≤ A(g) ≤ 300.

Step-by-step explanation:

The function A(g) = 100q represents the area in square feet that q quarts of paint cover. The given information states that a quart of paint covers 100 square feet of trim. Therefore, the function is giving us the area that the given amount of paint will cover. To determine the reasonable domain and range for this function, we need to consider the limitations of the problem.

The domain represents the valid values for the independent variable, q. In this case, the number of quarts of paint cannot be negative or greater than the available amount of paint, which is 3 quarts. Therefore, a reasonable domain for this function would be 0 ≤ q ≤ 3.

The range represents the valid values for the dependent variable, A(g), which is the area. Since each quart of paint covers 100 square feet, the area covered cannot be negative or exceed the total area that can be covered by the available amount of paint. Therefore, a reasonable range for this function would be 0 ≤ A(g) ≤ 300.