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

Secondary 4-5

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 Where $h$ and $k$ are Non-Zero

Example Where $h=0$ and $k=0$

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

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

Solving Problems Using Step Functions (Greatest Integer)

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Example Where $h=0$ and $k=0$
Example Where $h$ and $k$ are Non-Zero
Exercise

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

See solution

Example Where hhh and kkk are Non-Zero

See solution

Exercise

Solving Problems Using Step Functions (Greatest Integer)

Example Where $h=0$ and $k=0$

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