Chapter 1.3, Problem 33E

Solution

To Sketch: Sketch the given function and find the domain and range of the function.

Given information:

  $s\left(x\right)=\mathrm{int}\left(\frac{x}{2}\right)$

Graph:

The graphical representation of $s\left(x\right)=\mathrm{int}\left(\frac{x}{2}\right)$ is as follows:

  

Find the domain and range:

From the graph $f\left(x\right)=\mathrm{int}\left(\frac{x}{2}\right)$ , it is clear that the domain is all real numbers and the range is all integers.

Thus, the domain and range are:

Domain: All real numbers: $\left(-\infty ,\infty \right)$ or $ℝ$

Range: All integers: $\mathbb{Z}$