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?
These are my options:
domain: 1<s<6
Range: 24<c(s)<144
domain: 0<s<6
range: 0<c(s)<144
domain: 24<c(s)<144
range: 1<s<6
domain: 0<c(s)<144
range: 0<s<6
It is hard for me to get the domain and range of this problem. Thanks.
To determine the domain and range of the function c(s) = 24s, we need to consider the restrictions and limitations imposed by the given problem.
1. Domain: The domain represents the valid inputs for the function. In this case, the function c(s) represents the number of cookies that can be made with s cups of sugar. Since you have 6 cups of sugar, the minimum value of s would be 0 (no sugar used) and the maximum value would be 6 (using all 6 cups of sugar). Therefore, the reasonable domain for this function is 0<s<6.
2. Range: The range represents the possible outputs or results of the function. The function c(s) = 24s calculates the number of cookies made using s cups of sugar. Since the relationship is directly proportional (more sugar, more cookies), the minimum number of cookies that can be made is 0 (using no sugar), and the maximum number would be 144 (using all 6 cups of sugar, which makes 24 * 6 = 144 cookies). Hence, the reasonable range for this function is 0<c(s)<144.
Based on these considerations, the correct options for the domain and range of the function c(s) = 24s are:
Domain: 0<s<6
Range: 0<c(s)<144