Question

Absolute value parent function please give basic formula. Graph/asymptotes should be identified and labeled,domain, range, table of short points

Answer 1

The absolute value function is

`f(x)=|x|=\begin{cases}x,x\ge0 \\ -x,x<0\end{cases}`

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

`\begin{gathered} \text{domain}=(-\infty,\infty)=\R \\ \text{range}=\lbrack0,\infty)=\mleft\lbrace y\in\R|y\ge0\mright\rbrace \end{gathered}`

Finally, notice that the function does not have any asymptotes.