A package of paper towels contains 3 rolls. Each package of paper towels costs $2.79.
A function, f(x), is written to represent the cost of purchasing x packages of paper towels.
What is the practical domain for the function f(x)?
The practical domain for the function f(x) would be the set of possible values for x that make sense in the given context.
In this case, the practical domain would be the set of non-negative integers, since you cannot purchase a fraction or a negative number of packages of paper towels.
Therefore, the practical domain for the function f(x) would be {0, 1, 2, 3, ...}.
To determine the practical domain for the function f(x), we need to consider the given information:
- Each package of paper towels contains 3 rolls.
- Each package of paper towels costs $2.79.
Now, let's analyze the problem and find the limitations on the variable x:
1. The number of packages of paper towels, x, cannot be negative, as it represents a quantity of physical products. So, x ≥ 0.
2. Since each package contains 3 rolls, the number of rolls, n, must be a multiple of 3. Therefore, n = 3x.
3. The cost of purchasing x packages of paper towels is given by the function f(x). Since each package costs $2.79, the cost of x packages would be 2.79 times x. Therefore, f(x) = 2.79x.
Combining these constraints, we can determine the practical domain for the function f(x):
x ≥ 0 (the number of packages cannot be negative).
So, the practical domain for the function f(x) is x ≥ 0.