please help me out with the making of graph of:
f(x)= lx-2l + lx-3l
​also find the range and domain of funct.! thank u in advance sir!
 

Dear Student,

$$\begin{gathered} \mathrm{Let} \mathrm{y}=\left|\mathrm{x}-2\right|+\left|\mathrm{x}-3\right| \\ \left(1\right) \mathrm{When} \mathrm{x}\le 2, \\ \mathrm{y}=-\left(\mathrm{x}-2\right)-\left(\mathrm{x}-3\right) \\ \Rightarrow \mathrm{y}=5-2\mathrm{x} \\ \left(2\right) \mathrm{When} 2\le \mathrm{x}\le 3, \\ \mathrm{y}=\left(\mathrm{x}-2\right)-\left(\mathrm{x}-3\right) \\ \Rightarrow \mathrm{y}=1 \\ \left(3\right) \mathrm{When} \mathrm{x}\ge 3 \\ \mathrm{y}=\mathrm{x}-2+\mathrm{x}-3 \\ \Rightarrow \mathrm{y}=2\mathrm{x}-5 \\ \mathrm{Now}, \mathrm{from} \mathrm{the} \mathrm{graph} \mathrm{it} \mathrm{is} \mathrm{clear} \mathrm{that} \mathrm{function} \mathrm{is} \mathrm{defined} \mathrm{for} \mathrm{all} \mathrm{real} \mathrm{values} \mathrm{so}, \mathrm{Domain}=\left(-\infty ,\infty \right) \mathrm{And} \mathrm{Range}= [1,\infty ) \end{gathered}$$


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