Question

Graph each function. Identify the domain and range.

$f\left(x\right)=\left[\right[x\left]\right]-1$

Short answer

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

The graph of the function is shown below:

Step-by-step solution

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 $f\left(x\right)=\left[\right[x\left]\right]-1$

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 it means it will produce only integer values.

Therefore, the range is the set of all integers.

Step-3 – Draw the table.

The symbol $\left[\right[x\left]\right]$ means the greatest integer less than or equal to $x$.

For example: $\left[\right[7.3\left]\right]=7 and \left[\right[-1.5\left]\right]=-2$

Therefore, the required table is:

Step-4 – Graph the function.

The graph of the function is: