Question

Graph each function. Identify the domain and range.

$f\left(x\right)=\left[x\right]-2$

Short answer

The graph of the equation $f\left(x\right)=\left[x\right]-2$is provided below.

The domain of the function is $\mathrm{ℝ}$and range is $\mathrm{\mathbb{Z}}$.

Step-by-step solution

Step-1 – Apply the concept of greatest integer function

The greatest integer function, written as $f\left(x\right)=\left[x\right]$ is defined as the greatest integer less than or equal to x.

Step-2 – Make a Table of values 

Make a table of values such that the values satisfy the equation $f\left(x\right)=\left[x\right]-2$.

Choose a value of x and find the corresponding value of $f\left(x\right)$.

Step-3 – Graph the tabled values

The dot denotes that point is included the graph and the circle denotes that point is not included in the graph.

Step-4 – Find domain and range

The domain is the set of values which makes the function well defined. The range is the set of values of dependent variable.

The function $f\left(x\right)=\left[x\right]-2$is defined for all real values.

The domain of the function is $\mathrm{ℝ}$and range is set of integers $\mathrm{\mathbb{Z}}$.