Algebra 2, 2008

 PAGE: 99 SET: Exercises PROBLEM: 1

The function is .

The above function is greatest integer function.

The symbol means the greatest integer less than or equal to x.

For example, because .

The function is .

Make the table of values to find ordered pairs that satisfy the equation.

In this case, it is easier to choose x values and then find the corresponding values for y.

 x (x, f(x)) (dot point) (x, f(x)) (circle point)

To draw the step function follow the steps.

1. Draw a coordinate plane.

2. Plot the points on the coordinate plane.

3. Then sketch the line segments, connecting the every two points (one dot point and one circle point) with a smooth line.

Note: A dot means that the point is include in the graph and a circle means that the point is not included in the graph.

Since x can be any real number, there is an infinite number of ordered pairs that can be graphed. All of them lie on the graph shown.

Notice that every real number is the x - coordinate of some point on the graph, so the domain is all real numbers

Also, every integer number is the y - coordinate of some point on the graph and the range is all integers.

The domain is all real numbers and range is all integers, and the function graph is

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