Step Function Intuition Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
Evaluate: (a) ⌊7.9⌋\lfloor 7.9 \rfloor, (b) ⌈4.1⌉\lceil 4.1 \rceil, (c) ⌊−0.5⌋\lfloor -0.5 \rfloor, (d) ⌈−3.2⌉\lceil -3.2 \rceil.

Solution

  1. 1
    (a) ⌊7.9⌋=7\lfloor 7.9 \rfloor = 7; (b) ⌈4.1⌉=5\lceil 4.1 \rceil = 5.
  2. 2
    (c) ⌊−0.5⌋=−1\lfloor -0.5 \rfloor = -1 (floor rounds toward −∞-\infty); (d) ⌈−3.2⌉=−3\lceil -3.2 \rceil = -3 (ceiling rounds toward +∞+\infty).

Answer

(a) 77, (b) 55, (c) −1-1, (d) −3-3
Floor always rounds down (toward −∞-\infty) and ceiling always rounds up (toward +∞+\infty). For negative numbers, these differ from rounding toward zero: ⌊−0.5⌋=−1\lfloor-0.5\rfloor=-1, not 00.

About Step Function Intuition

A step function is piecewise constant — it takes a fixed value on each of several intervals, jumping abruptly at the interval boundaries.

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More Step Function Intuition Examples

Example 1 easy

Evaluate the floor function [formula] at [formula], [formula], and [formula]. Then describe the grap

Example 2 medium

A parking garage charges [formula]3[formula][formula] for each additional hour (or part). Write and

Example 4 hard

Define [formula]. Find all [formula] in [formula] where [formula], and sketch [formula] on [formula]

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Related Concepts

Piecewise Function