Practice Step Function Intuition in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A step function is piecewise constant — it takes a fixed value on each of several intervals, jumping abruptly at the interval boundaries.
Imagine a staircase: the height is constant on each step, then jumps up (or down) at each transition. Postal rates, grade cutoffs, and floor() all create steps.
Example 1
easyEvaluate the floor function f(x) = \lfloor x \rfloor at x = 3.7, x = -2.1, and x = 5. Then describe the graph on [0, 4].
Example 2
mediumA parking garage charges \3 for the first hour (or part thereof) and \2 for each additional hour (or part). Write and evaluate the cost function for t = 0.5, 1, 1.2, and 3.9 hours.
Example 3
easyEvaluate: (a) \lfloor 7.9 \rfloor, (b) \lceil 4.1 \rceil, (c) \lfloor -0.5 \rfloor, (d) \lceil -3.2 \rceil.
Example 4
hardDefine f(x) = \lfloor 2x \rfloor. Find all x in [0, 2] where f(x) = 3, and sketch f on [0,2].