Question

Graph each function. State the domain and range.

$\mathit{f}\mathbf{\left(}\mathbf{x}\mathbf{\right)}\mathbf{=}\mathbf{\left[}\mathbf{2}\mathbf{x}\mathbf{\right]}$

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 $f\left(x\right)=\left[x\right]$, where $f\left(x\right)$is the greatest integer not greater than $x$.

For example, $\left[6.8\right]=6$, because 6 is the greatest integer that is not greater than $6.8$.

Type of Graph : disjointed line segments.

Step 2. Make a table for the given function.

Construct a table for $f\left(x\right)=\left[2x\right]$by taking some values of x.

$x$	$2x$	$f\left(x\right)=\left[2x\right]$
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 $x$and $f\left(x\right)$on a graph,

For the domain, see the $x$-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.