7. Piecewise Functions
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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:
Interval | f(x)=[[x]] |
---|---|
-4≤x<-3 | -4 |
-3≤x<-2 | -3 |
-2≤x<-1 | -2 |
-1≤x<0 | -1 |
0≤x<1 | 0 |
1≤x<2 | 1 |
2≤x<3 | 2 |
3≤x<4 | 3 |
Let's graph the function for -4≤x<4.
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.
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.
The graph is a series of horizontal line segments. Therefore, the function f(x)=[[x]] is a step function.