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?
cookies= 24s
What domain and range is reasonable for this function?
To set up and solve this problem, we first need to understand the given information and the function presented.
Given:
- 6 cups of sugar
- It takes 1 cup of sugar to make 24 cookies
- Function c(s) = 24s represents the number of cookies, c, that can be made with s cups of sugar
Now, let's start by finding the domain and range for the function c(s) = 24s.
Domain represents the set of all possible input values for a function. In this case, the input is the number of cups of sugar (s). Since there are 6 cups of sugar available, it would be reasonable to assume that the domain includes all non-negative values up to or equal to 6. In mathematical notation, the domain can be expressed as: 0 ≤ s ≤ 6.
Range represents the set of all possible output values for a function. In this case, the output is the number of cookies (c) that can be made using a certain amount of sugar. The range will depend on the amounts of sugar used, which can be calculated by evaluating the function. Since the function c(s) = 24s is a linear equation, the range will be all non-negative multiples of 24. In mathematical notation, the range can be expressed as: c ≥ 0 (where c is a multiple of 24).
To find the range, you could evaluate the function for different values of s within the domain. However, since the range is already known to be non-negative multiples of 24, you could simply say that the range is c ≥ 0, where c is a multiple of 24.
To summarize:
- The domain for the function c(s) = 24s is 0 ≤ s ≤ 6.
- The range for the function c(s) = 24s is c ≥ 0, where c is a multiple of 24.