Please show me how to set up and solve:
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 is reasonable for the function?
math - bobpursley, Wednesday, April 18, 2012 at 11:08am
cookies= 24s
math - Jane, Wednesday, April 18, 2012 at 11:12am
What domain and range is reasonable for this function?
To determine the domain and range of the given function c(s) = 24s:
1. Domain: The domain represents the set of possible values for the input variable, which in this case is the number of cups of sugar, s. Since the problem states that you have 6 cups of sugar, it would be reasonable to assume that the domain includes values from 0 to 6, as you cannot have negative cups of sugar, and it is unlikely to have more than 6 cups if that is the given amount.
Therefore, the domain of the function c(s) = 24s is reasonable for values of s between 0 and 6, inclusive: D = {0, 1, 2, 3, 4, 5, 6}.
2. Range: The range represents the set of possible values for the output variable, which in this case is the number of cookies, c, that can be made with a given number of cups of sugar. Since we know that it takes 1 cup of sugar to make 24 cookies, the range will depend on the number of cups of sugar used.
To find the range, we can substitute the possible values of s (0, 1, 2, 3, 4, 5, 6) into the function c(s) = 24s and calculate the corresponding values for c.
c(0) = 24 * 0 = 0 cookies
c(1) = 24 * 1 = 24 cookies
c(2) = 24 * 2 = 48 cookies
c(3) = 24 * 3 = 72 cookies
c(4) = 24 * 4 = 96 cookies
c(5) = 24 * 5 = 120 cookies
c(6) = 24 * 6 = 144 cookies
Therefore, the range of the function c(s) = 24s is reasonable for values between 0 and 144 cookies: R = {0, 24, 48, 72, 96, 120, 144}.