Question

Graph each function. State the domain and range.

$\mathit{f}\mathbf{\left(}\mathbf{x}\mathbf{\right)}\mathbf{=}\mathbf{|}\mathbf{2}\mathbf{x}\mathbf{-}\mathbf{2}\mathbf{|}$

Short answer

The domain is all real numbers and the range is non-negative real numbers i.e.,

$\mathbf{\{}\mathbf{y}\mathbf{:}\mathbf{y}\mathbf{\ge }\mathbf{0}\mathbf{\}}$

Step-by-step solution

Step 1. State the concept for absolute value function.

An absolute value function is a function that contains an algebraic expression within absolute value symbols. The absolute value of a number is its distance from 0 on the number line.

$f\left(x\right)=\left|x\right|=\left\{\begin{array}{c}x;x>0\\ -x;x\le 0\end{array}\right\}$

Step 2. Solve for x.

Since $f\left(x\right)$cannot be negative , so the minimum point of the graph will be where

$f\left(x\right)=0$

$\begin{array}{c}f\left(x\right)=|2x-2|\\ f\left(x\right)=\pm (2x-2)=0\\ 2x-2=0\\ 2x=2\\ x=1\end{array}$

f(x)Step 3. Make a table for the given function.

Construct a table for by taking some values ofx.