You have 11 cups of flour. It takes 1 cup of flour to make 24 cookies. The function c(f) = 24f represents the number of cookies, c, that can be made with f cups of flour. What domain and range are reasonable for the function?
Wendy, you are giving consistently wrong answers, please take a break.
Domain: flour, zero to 1000 cups, or whatever maximum you wnat to figure.
Range: cookies: zero to 24 times your max domain.
if 11 cups of sugar were used, how many cups of flour would be needed?
The domain of the function c(f) = 24f represents the possible inputs, or values of f, for the function. In this case, the number of cups of flour, f, can range from 0 to 11, as that is the amount of flour available.
Thus, the domain of the function is [0, 11].
The range of the function c(f) = 24f represents the possible outputs, or values of c, for the function. In this case, the number of cookies, c, can be any positive whole number since you cannot have a fraction of a cookie.
Thus, the range of the function is [0, ∞) or {0, 24, 48, 72, ...}.
To determine the domain and range of the function c(f) = 24f, we need to consider the context of the problem.
In this case, the number of cookies, c, is dependent on the number of cups of flour, f. The domain of the function represents the possible values for the input (cups of flour) that make sense in this context. The range, on the other hand, represents the possible values for the output (number of cookies).
Domain:
Since you have 11 cups of flour, the number of cups of flour, f, should be a non-negative number (since we can't have negative cups of flour). Additionally, it should not exceed the amount of flour you have, so the maximum value for f in this case is 11. Therefore, the reasonable domain for this function would be 0 ≤ f ≤ 11.
Range:
The number of cookies, c, depends on the number of cups of flour, f, according to the equation c(f) = 24f. Since the number of cookies is a result of multiplying the number of cups of flour by 24, it will always be a positive integer, as long as f is a positive integer. Therefore, the reasonable range for this function would be a set of positive integers, where c ≥ 0.
In summary:
Domain: 0 ≤ f ≤ 11
Range: c ≥ 0 (positive integers)