Q5. - Algebra 2

Question

Graph $f\left(x\right)=\left|x-1\right|$. Identify the domain and range

Step-by-Step Solution

Answer

Domain of $f\left(x\right)=R$

Range of  $f\left(x\right)=R^{+}=\left[0,\infty \right]$

Step-1 –Defining the function

$\begin{array}{l}f\left(x\right)=\left|x-1\right|\\ =\left\{\begin{array}{l}x-1,ifx\ge 1\\ 1-x,ifx<1\end{array}\right\}\end{array}$

Step-2 &ndash;Determining the domain of f ( x )

Domain is the point where the value of $x$ is defined

So, Domain of $f=R$

Step-3 &ndash;Determining the Range of f(x)

Points where $f\left(x\right)$is defined is called range

So, $f\left(x\right)$is defined when it is greater than $\text{'}0\text{'}$

Then, $x-1\ge 0$

Range of $f\left(x\right)=R^{+}=\left[0,\infty \right]$

Step-4 &ndash;Plotting the Graph of f(x)