You have 6 cups of sugar. It takes 1 cup of sugar to make 24 cookies. The function c(s) = 24s represents the number of cookies, c, that can be made with s cups of sugar. What domain and range are reasonable for the function?

(I know that you get 144 cookies from 6 cups of sugar.)
The domain and range are written in inequality such as: Range: 1<s<6
Domain: 24<c(s)<144. This may not be correct answer, but it is how to set it up.

Domain = All real values of s:

-Infinity < S < +Infinity.

To determine the domain and range of the function c(s) = 24s, let's break it down step by step.

Domain refers to the set of all possible inputs for the function. In this case, the input is the number of cups of sugar, denoted by s. Since we know that you have 6 cups of sugar, a reasonable domain would be the values of s that are equal to or less than 6. Therefore, we can write the domain as s ≤ 6.

Range, on the other hand, refers to the set of all possible outputs for the function. In this case, the output is the number of cookies, denoted by c. The function c(s) = 24s tells us that the number of cookies is determined by multiplying the number of cups of sugar by 24. Since the number of cookies cannot be negative, the range should be c ≥ 0.

Now, let's calculate the actual values for the range. We know that with 6 cups of sugar, you can make 144 cookies (as you mentioned). So, we have the maximum value for the range as c ≤ 144.

Putting it all together, the domain is s ≤ 6 and the range is 0 ≤ c ≤ 144.

Please note that the inequalities you provided in your question (Domain: 24 < c(s) < 144 and Range: 1 < s < 6) do not accurately represent the relationship between the number of cups of sugar and the number of cookies, as the values in the parentheses should be switched.