Solving Problems Involving the Step Function (the Greatest Integer Function)

Concept sheet | Mathematics

To solve a problem involving the greatest integer function, it is important to understand the function well. It is also important to learn how to solve the equation algebraically for a problem without context. For more details, see the following concept sheet: Solving a Step Function Equation.

Example Where |h=0| and |k=0|

Example

Justin needs a lawyer to settle a dispute with his landlord regarding certain clauses in his lease. He contacts a lawyer specializing in property leases. The lawyer's fees are the following: for each partial or full period of |15| minutes, the lawyer charges |\$ 45|. Fortunately, taxes are included.

a) If studying the case requires |3| hours and |24| minutes, how much will it cost Justin?

b) When the case is completely settled, Justin calculates that he paid a total of |\$ 2\ 700| in fees. For how many hours did the lawyer bill him for?

See solution

Example Where |h| and |k| are Non-Zero

Example

Dominik rents movies from his favorite video store once a week. Unfortunately, he has the annoying habit of not returning his films on time. A movie costs |\$ 2.50| on the first day. The film must be returned after one day or else he must pay a late fee of |\$ 3.00| per day.

a) Determine the equation of the function modeling this situation and draw the graph.

b) How much does Dominik have to pay if he brings back his film |6| days later?

See solution

Exercise

Exercise

Solving Problems Using Step Functions (Greatest Integer)

Mathematics Secondary4-5