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Home > INT2 > Chapter 9 > Lesson 9.4.1 > Problem 9-142


Jill has a business organizing children’s birthday parties. For a party with up to six children, she charges . She charges another for each additional guest.

  1. Write a piecewise-defined function to represent the money Jill receives for organizing a birthday party for children. Be sure to include any restrictions on the domain. Check your function using several different numbers of children.

    For to children the cost is a constant function.

    Use this pattern to write a rule for seven or more children.

  1. The party favors and treats cost per child. Write a function to represent the expenses for a party for children.

  2. What is Jill’s net income, , from a party for children in terms of and ? That is, how much money will she have after she pays for the party favors and treats?

    Write an expression that subtracts her expenses from her income.

  1. Write a piecewise-defined function for including restrictions on the domain, and check it by testing values for different numbers of children.

    Combine the answers from parts (a) − (c) into a piecewise function.