Step Functions and the Greatest Integer Function Worksheet with Answer Key

What's on the worksheet

1. Evaluate each floor or ceiling expression.
   \left\lfloor \dfrac{50}{7} \right\rfloor\lceil -0.9 \rceil + \lfloor 0.9 \rfloor\left\lfloor -\dfrac{17}{5} \right\rfloor\lfloor \sqrt{30} \rfloor\lceil 2.5 \rceil \cdot \lfloor -2.5 \rfloor
2. Find every x that makes each equation true, or write no solution.
   \lfloor x \rfloor + 4 = 12\lfloor x \rfloor - 1 = 6\lfloor x \rfloor^2 = 4\lceil x - 2 \rceil = 5\lfloor 5 - x \rfloor = 2
3. Solve each inequality and write it without floor or ceiling.
   \lfloor x \rfloor > 3\lfloor x \rfloor \le -2\lceil x \rceil < 1\lfloor x \rfloor \ge 2.5
4. Write a floor function as a piecewise function on a given domain.
5. River ferry: explain why the crossings use a ceiling, then answer questions.
6. Bike-share plans: compare the cost of two pricing plans by ride length.
7. Find when floor of 2x differs from twice the floor of x.