Q. 43 - Algebra 2

Question

Graph each function. Identify the domain and range.

$f\left(x\right)=\left|\left[\right[x\left]\right]\right|$

Step-by-Step Solution

Answer

The domain of the function is all real numbers and range is all nonnegative whole numbers.

The graph of the function is shown below:

Step 1. Domain and range of the function.

The domain of the function is the set of all input values and range of the function is the set of all output values.

Step 2. Determine the domain and range

Consider the given function $f\left(x\right)=\left|\left[\right[x\left]\right]\right|$

It can be observed that the domain of the function is the set of all real values because the function can take any value of x.

Here, the function is greatest integer as well as absolute value it means it will produce all nonnegative whole numbers.

 

Therefore, the range is the set of all nonnegative whole numbers.

Step 3. Draw the table.

Make the table for different value of x.

x	y
$-3\le x<2$	$3$
$-2\le x<1$	2
$-1\le x<0$	1
$0\le x<1$	0
$1\le x<2$	1

Step 4. Graph the function.

The graph of the function is: