Please explain how to solve:
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?
My choices are:
Domain Range
0¡Üc(f)¡Ü264 0¡Üf¡Ü11
0¡Üf¡Ü11 0¡Üc(f)¡Ü264
24¡Üc(f)¡Ü264 1¡Üf¡Ü11
1¡Üf¡Ü11 24¡Üc(f)¡Ü264
To determine the reasonable domain and range for the function c(f) = 24f, we need to consider the given information about cups of flour and cookies.
Domain represents the set of possible input values for the function, which in this case is the number of cups of flour. We are told that you have 11 cups of flour, so the reasonable domain would be 0 ≤ f ≤ 11. This means that the number of cups of flour cannot be negative and cannot exceed the 11 cups you have.
Range represents the set of possible output values for the function, which in this case is the number of cookies. We know that it takes 1 cup of flour to make 24 cookies. So, for each cup of flour, we can make 24 cookies. Hence, the reasonable range would be 0 ≤ c(f) ≤ 264 (24 cookies from 11 cups of flour).
From the provided choices, the correct answer is:
Domain: 0 ≤ f ≤ 11
Range: 0 ≤ c(f) ≤ 264