How to graph the greatest integer function?
Understand the Problem
The question is asking for guidance on how to create a graph of the greatest integer function, which is often represented as ⌊x⌋. This function maps any real number to the largest integer less than or equal to that number. To graph it, we need to plot points for different values of x and connect them appropriately.
Answer
Plot horizontal segments [n, n+1) with closed circles at n and open circles at n+1.
To graph the greatest integer function, plot horizontal line segments from [n, n+1) with a closed circle at n and an open circle at n+1 for each integer n.
Answer for screen readers
To graph the greatest integer function, plot horizontal line segments from [n, n+1) with a closed circle at n and an open circle at n+1 for each integer n.
More Information
The graph of the greatest integer function resembles steps, hence it is also called the step function. Each 'step' starts at an integer and goes up to but does not include the next integer.
Tips
Common mistakes include placing open and closed circles incorrectly and misunderstanding the interval notation.
