The absolute value function is
[tex]f(x)=|x|=\begin{cases}x,x\ge0 \\ -x,x<0\end{cases}[/tex]
Thus, the graph of the absolute value function consists of two rays that intercept on the origin, as shown in the image below
Using a table for relevant values,
x f(x)
-3 3
-2 2
-1 1
0 0
1 1
2 2
3 3
Notice that there is no limit to the value that x can take; on the other hand, f(x) cannot take any negative values. Then, Domain and Range
[tex]\begin{gathered} \text{domain}=(-\infty,\infty)=\R \\ \text{range}=\lbrack0,\infty)=\mleft\lbrace y\in\R|y\ge0\mright\rbrace \end{gathered}[/tex]
Finally, notice that the function does not have any asymptotes.
