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
Look at what you wrote:
3x <= x <= 1000
Does that make sense?
How about
0 <= 3x <= 1000
0 <= x <= 333.3
or, in terms of whole presents,
0 <= x <= 333
and of course the range is thus
0 <= f(x) <= 1000
The domain for this problem can be described using the inequality 3x ≤ x ≤ 1000. This means that the number of presents, x, must be greater than or equal to 0 and less than or equal to 1000 in order for the function to be valid.
To describe the domain for this problem, we need to determine the possible values for x, which represents the number of presents wrapped.
Given that they only have enough wrapping paper to wrap 1000 presents, the maximum number of presents they can wrap is 1000. However, there is no minimum number of presents mentioned in the problem, so x can be any non-negative number.
Therefore, the domain for this problem can be described using inequality notation as:
0 ≤ x ≤ 1000
This means that x can take on any value between 0 and 1000 (inclusive).
Now let's move on to the range.
The range describes the possible values of f(x), which represents the amount of money the club will earn.
Since the function f(x) = 3x describes the amount of money earned for wrapping x presents, the range of f(x) will depend on the values of x.
Since x represents the number of presents wrapped, it must be a non-negative integer. Therefore, the smallest value of x is 0.
Substituting x = 0 into the function f(x) = 3x, we get f(0) = 3(0) = 0. This means that if no presents are wrapped (x = 0), the club will earn $0.
As for the maximum value of f(x), it corresponds to the maximum value of x, which is 1000 in this case. Substituting x = 1000 into the function f(x) = 3x, we get f(1000) = 3(1000) = 3000. This means that if 1000 presents are wrapped, the club will earn $3000.
Therefore, the range for this problem can be described using inequality notation as:
0 ≤ f(x) ≤ 3000
This means that the amount of money earned (f(x)) can take on any value between $0 and $3000 (inclusive).