[tex]\begin{gathered} y-\text{interceptions are given when x=0. In this case:} \\ y(0)=\text{ -2|0-1|+4} \\ y(0)=-2(1)+4 \\ y(0)=-2+4 \\ y(0)=2\text{ this is the y-interception} \\ \text{Now, x}-\text{interceptions are given when y=0. In this case:} \\ 0=\text{-2|x-1|+4} \\ \Rightarrow\text{-2|x-1|}=-4 \\ \text{|x-1|}=\frac{-4}{-2} \\ \text{|x-1|}=\frac{4}{2} \\ \text{|x-1|}=2 \\ \text{The absolute value implies 2 cases: a) when x-1=2 and b) x-1=-2.} \\ \text{case a). x-1=2 }\Rightarrow x=2+1\Rightarrow x=3 \\ \text{case b) x-1=-2}\Rightarrow x=-2+1\Rightarrow x=-1 \\ \text{Hence x-intercepts are x= -1 and x=3} \end{gathered}[/tex]
