HELP please, Domain & range

0 < S <= 30

3500 < C <= 7400

Step-by-step explanation:

the domain is the interval of values for x (the input variable), for which the function is defined valid to process them.

the range is the interval of y values, the possible results of the function.

as the question writes, C is a function of S. so, our input variable is called S (instead of the usual x).

C(S) = 130S + 3500

this function will be valid for what values of S ?

given the context, are negative values ok for S ?

no, negative transportation amounts don't make sense here.

is 0 a valid value ?

no, they would be driving an empty transport.

and it is said that they can transport up to 30 tons.

so, our S can only be in the interval 0 < S <= 30

that is the domain of the function describing the amount of sugar transported.

the range is now the functional value interval, the interval for y, the calculated cost for transported sugar.

it starts with the smallest possible value, which we simulate by using x=0 again (which is just outside of our valid domain, but really only "just", as everything bigger than 0, no matter how small, is valid).

C(0) = 130×0 + 3500 = 3500

the range starts there but excludes that particular value, as we excluded 0 in the domain.

and the biggest value for the function is clearly, when they transport the maximum capacity : 30 tons.

C(30) = 130×30 + 3500 = 3900 + 3500 = 7400

so, the range is

3500 < C <= 7400

true

explanation: