There are 98 international units of vitamin D in 1 cup of milk. The function V(c)=98c represents the amount V(c) of vitamin D, in IUs, you get from c cups of milk. You have a 16 cup jug of milk. What is a reasonable domain and range for this function?

How do I set up the equation? I so confused!....I have no idea if this is right....c< or =16,V(c)< or =1,568

Answer: 0<c<16,0<V(c)<1,568

Close. You do need to specify that c is not negative, so the domain is 0 <= c <= 16, or the interval [0,16].

The range would then be [0,1568].

There is no equation, just a couple of expressions.

thank you you helped allot

Well, my friend, you're on the right track! The equation you mentioned is indeed correct. However, let's break it down a bit further to fully understand it.

The given function V(c) = 98c represents the amount of vitamin D you get from c cups of milk. In this equation, c represents the number of cups of milk you have.

Now, the domain of the function is the set of all possible values for c. In this particular case, since you have a 16 cup jug of milk, it would be reasonable to assume that the maximum number of cups you can have is 16. Therefore, the domain would be c ≤ 16 (or c ≤ 16 cup, if you prefer to clarify the unit).

On the other hand, the range of the function represents the possible values for V (the amount of vitamin D). Since V is directly proportional to c (the number of cups), the maximum amount of vitamin D you can get should occur when you have the maximum number of cups. In this case, the maximum number of cups is 16, so the maximum value for V would be 98 times 16, which is 1,568 IU. Therefore, the range would be V(c) ≤ 1,568 IU.

So, in summary, the reasonable domain for this function would be c ≤ 16 (c being the number of cups) and the reasonable range would be V(c) ≤ 1,568 IU (V(c) being the amount of vitamin D in International Units).

I hope that clears things up for you! If you have any more questions or need further clarification, feel free to ask.

To set up the equation for this function, you need to understand the concept of domain and range.

The domain of a function represents all possible values for the input (in this case, the number of cups of milk, c). In this situation, you have a 16 cup jug of milk, so the reasonable domain for this function would be c ≤ 16. This means that the number of cups of milk cannot exceed 16.

The range of a function represents all possible values for the output (in this case, the amount of vitamin D in International Units, V(c)). The function V(c) = 98c indicates that the amount of vitamin D increases linearly with the number of cups of milk. Since we know that there are 98 international units of vitamin D in 1 cup of milk, the amount of vitamin D you can get will depend on the total number of cups of milk you consume. Therefore, the reasonable range for this function would be V(c) ≤ 98c.

Now let's evaluate these constraints for the given example:
- Domain: c ≤ 16. In this case, the statement "c ≤ 16" means that the number of cups of milk is less than or equal to 16. Since the jug contains 16 cups of milk, any value of c less than or equal to 16 would be valid in this domain.
- Range: V(c) ≤ 98c. Here, "V(c) ≤ 98c" states that the amount of vitamin D (V(c)) should be less than or equal to 98 times the number of cups of milk (c). Since the jug contains 16 cups, the maximum amount of vitamin D you can get is 98 times 16, which equals 1,568 IU. Therefore, the range for this function would be V(c) ≤ 1,568.

To summarize:
Domain: c ≤ 16
Range: V(c) ≤ 1,568