Big Ideas Math Algebra 1, 2015
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Big Ideas Math Algebra 1, 2015 View details
7. Piecewise Functions
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Exercise 53 Page 224

To find the output of the greatest integer function, round the input value down to the nearest integer.

Piecewise Function? Yes.
Step Function? Yes.
Explanation: See solution. Graph:

Diagram with the graph of the greatest integer function.
Practice makes perfect
The output of the greatest integer function, is the greatest integer less than or equal to the input value To help us understand how this function works we will first look at a few examples.
We can think of it as rounding down the input value to the nearest integer. This results in a function that is divided into multiple intervals, where the function is constant within an interval.
Interval

Let's graph the function for

Diagram with the graph of the greatest integer function.

Recall that a closed dot corresponds to an end value that is included and an open dot means that the end value is not included.

Is It a Piecewise Function?

A piecewise function is any function defined by two or more equations, each applying to a different part of the domain. To show that the greatest integer function is a piecewise function, we can write the equation as constant functions defined on intervals.

Is It a Step Function?

A step function, on the other hand, is a special type of piecewise function characterized by a series of horizontal line segments. Let's once more study the graph of the greatest integer function.

Diagram with the graph of the greatest integer function.

The graph is a series of horizontal line segments. Therefore, the function is a step function.