STEP FUNCTION
Definition Of Step Function
A step function is a special type of function whose graph is a series of line segments.
The graph of a step function looks like a series of small steps.
Video Examples: The Unit Step Function
Example of Step Function
The figure below shows the graph of the step function f(x) = [[x - 1]], which is a greatest integer function.
Another name for this kind of graph is a piecewise linear graph, because the graph consists of small line segments.
Solved Example on Step Function
Ques: Which of the following is a step function?
(i) f(x) = b
(ii) f(x) = |x|
(iii) f(x) = [[x]]
Choices:
A. only (i)
B. only (ii)
C. only (iii)
D. all the three
Correct Answer: C
Solution:
Step 1: Among the functions listed, only f(x) = [[x]] is the step function. [[ ]] indicates that its a Greatest Integer Function that rounds any number down to the nearest integer.
Step 2: So, f(x) = [[x]] is a step function.
Quick Summary
- Step functions have graphs resembling steps.
- A common example is the greatest integer function (floor function).
- Step functions are piecewise constant.
🍎 Teacher Insights
Use real-world examples like pricing tiers or postage rates to illustrate step functions. Emphasize the concept of discontinuity.🎓 Prerequisites
- Functions
- Integers
- Graphing
Check Your Knowledge
Q1: Which of the following is a step function?
Frequently Asked Questions
Q: What is the greatest integer function?
A: The greatest integer function, denoted by [[x]] or floor(x), returns the largest integer less than or equal to x.
Q: Are all piecewise linear functions step functions?
A: No, only piecewise linear functions where each piece is a horizontal line segment are step functions.