Hector’s service club is raising money by wrapping presents in the mall. The function f(x) = 3x describes the amount of money, in dollars, the club will earn for wrapping x presents. They only have enough wrapping paper to wrap 1000 presents.

Describe the domain and range for this problem using appropriate notation.
Domain: 3x < or equal to x < or equal to 1000
Range: ?

Domain: 0 ≤ x ≤ 1000 (since they can't wrap a negative or more than 1000 presents)

Range: 0 ≤ f(x) ≤ 3000 (since the amount of money earned can't be negative or more than $3000)

The range for this problem can be described as the set of possible values for the amount of money the club will earn. Since the function f(x) = 3x represents the amount of money earned for wrapping x presents, the range would be the set of all possible values of 3x.

In this case, the domain for this problem has already been provided as x < or equal to 1000. So, the range would be the set of values of 3x where x is less than or equal to 1000. In notation, this can be written as:

Range: {3x | x ≤ 1000}

Here, the vertical bar (|) represents "such that" and the inequality x ≤ 1000 states the condition for x.

To describe the domain and range for this problem, we need to consider the conditions and limitations provided.

Domain: The domain represents the possible values for the variable "x" in the function, which in this case refers to the number of presents wrapped. The conditions state that "the club will earn money for wrapping x presents" and "they only have enough wrapping paper to wrap 1000 presents."

Since the function f(x) = 3x describes the amount of money earned for wrapping x presents, the domain must take into account the number of presents that can actually be wrapped. Therefore, the domain for this problem can be described using appropriate notation as:

Domain: 0 <= x <= 1000

This means that the number of presents wrapped can range from 0 to 1000, including both 0 and 1000.

Range: The range represents the possible values for the output of the function, which in this case is the amount of money earned. Since the function f(x) = 3x directly describes the amount of money earned for wrapping x presents, the range can be any positive real number.

Therefore, the range for this problem is:

Range: f(x) > 0, where "f(x)" represents the amount of money earned.

In summary, the domain is 0 <= x <= 1000, and the range is f(x) > 0.