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Mobile App Chapter 4: Q52. (page 274)
Graph each function. State the domain and range.
Short Answer
The domain is all real numbers and the range is all integers.
Step by step solution
Step 1. State the concept for step function.
The graph of a step function is a series of line segments. Because each part of a step function is linear, this type of function is called a piecewise-linear function. One example of a step function is the Greatest Interger Function, written as , where is the greatest integer not greater than .
For example, , because 6 is the greatest integer that is not greater than .
Type of Graph : disjointed line segments.
Step 2. Make a table for the given function.
Construct a table for by taking some values of x.
0 | 0 | 0 |
0.25 | 0.5 | 0 |
0.5 | 1 | 1 |
0.75 | 1.5 | 1 |
1 | 2 | 2 |
1.5 | 3 | 3 |
2 | 4 | 4 |
2.5 | 5 | 5 |
3 | 6 | 6 |
Step 3. Plot the graph.
Plot the values of and on a graph,
For the domain, see the -coordinate values. As the dots and circles overlap, the domain is all real numbers .
For range, see the y-coordinate values. So, the range is all integers.
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