Question

Suppose the function E(c) represents the earnings of a volleyball team from selling cupcakes. Describe an appropriate domain of this function. Include a description of the kinds of numbers in the domain as well as any limitations on their values.

Answer 1

When we have a function y = f(x) we define the domain as the set of the values of x, and the range as the set of the values of y.

In this case we have the function:

E(c) where c represents the number of cupcakes sold by the team.

In this case, the domain will be the possible values that c can take.

The restrictions are:

c ≥ 0.

They can not sell a negative number of cupcakes.

c must be an integer because they can not sell a 0.342 of a cupcake, so the domain is discrete.

c may have an upper limit (for example, if they made 500 cupcakes, they can not sell more than 500) But we do not know any upper limit, so we can ignore this restriction.

Then we can define the domain as:

D = {0, 1, 2, 3, ...}